Real and Complex Submanifolds

Name: Real and Complex Submanifolds | Daejeon, Korea, August 2014
Brand: Springer
Price: 149.79 EUR
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Daejeon, Korea, August 2014

Young Jin Suh Jürgen Berndt Yoshihiro Ohnita Byung Hak Kim Hyunjin Lee(Editor)

Springer (Publisher)

1st Edition

Published on 5. December 2014

XII, 526 pages

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978-4-431-55215-4 (ISBN)

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Content

Intro
Preface
Organization
Committees
Contents
Part I Plenary Talks
Generalizations of the Catenoid and the Helicoid
1 Historical Remarks
2 Quasi-umbilicity
3 Generalized Catenoids
4 Lagrangian Catenoids
5 A Generalized Helicoid
6 A Lagrangian Helicoid
References
Harmonic Functions and Parallel Mean Curvature Surfaces
1 Introduction
2 Surfaces in a Complex Space Form
3 Known Results
4 The Case Where a ?
References
A New Technique for the Study of Complete Maximal Hypersurfaces in Certain Open Generalized Robertson-Walker Spacetimes
1 Introduction
2 Parabolicity of Riemannian Manifolds
3 Set Up
4 Parabolicity of Spacelike Hypersurfaces
5 The Restriction of the Warping Function on M
6 Uniqueness Results in the Parametric Case
7 Calabi-Bernstein Type Problems
References
Totally Geodesic Submanifolds of Riemannian Symmetric Spaces
1 Introduction
2 Totally Geodesic Submanifolds
3 Riemannian Symmetric Spaces
4 Lie Triple Systems
5 The Index of Riemannian Symmetric Spaces
References
Canonical Connection on Contact Manifolds
1 Introduction
2 Review of the Canonical Connection of Almost Kähler Manifold
3 Definition of the Contact Triad Connection and Its Consequences
4 Proof of the Uniqueness of the Contact Triad Connection
5 Properties of the Levi-Civita Connection on Contact Manifolds
6 Existence of the Contact Triad Connection
6.1 Modification 1
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1
6.2 Modification 2
tmp
2
References
Recent Progress in Isoparametric Functions and Isoparametric Hypersurfaces
1 Introduction
2 Exotic Spheres and Isoparametric Functions
3 Yau Conjecture on the First Eigenvalue and Isoparametric Foliations
4 Related Topics and Applications
References
Part II Invited Talks
Information Geometry of Barycenter Map
1 Introduction
2 Barycenter and Barycenter Map
3 Fibre Space Structure of P+(?X, d ?)
4 Barycentrically Associated Maps
References
Stability of Complete Minimal Lagrangian Submanifold and L2 Harmonic 1-Forms
1 Introduction
2 Proof of Theorem 1
3 Surface case
References
Bonnesen-Style Symmetric Mixed Isoperimetric Inequality
1 Introductions and Preliminaries
2 The Containment Measure
3 The Symmetric Mixed Isoperimetric Inequality
4 Reverse Bonnesen Style Symmetric Mixed Inequalities
References
Cho Operators on Real Hypersurfaces in Complex Projective Space
1 Introduction
2 Case of Shape Operator
3 Case of Structure Jacobi Operator
References
Geometry of Lagrangian Submanifolds Related to Isoparametric Hypersurfaces
1 Introduction
2 Lagrangian Submanifolds of Symplectic and Kähler Manifolds
3 Isoparametric Hypersurface Geometry and Lagrangian Submanifolds of Complex Hyperquadrics
4 Hamiltonian Stability of the Gauss Images of Isoparametric Hypersurfaces and Further Problems
References
Isometric Deformations of Surfaces with Singularities
1 Introduction
2 Isometric Deformations of Regular Surfaces
3 Isometric Deformations of Cuspidal Edges
4 Isometric Deformations of Cross Caps
References
Part III Contributed Talks
Beyond Generalized Sasakian-Space-Forms!
1 Introduction
2 Preliminaries
3 Generalized Sasakian-Space-Forms
4 Generalized S-Space-Forms
5 Generalized (?,µ)-Space-Forms
6 Semi-Riemannian Generalized Sasakian-Space-Forms
References
Some Geometric Aspects of the Hessian One Equation
1 Introduction
2 The Conformal Structure
3 Allowing Singularities
3.1 Prescribing Singular Curves
3.2 Isolated Singularities
4 Global Results
4.1 The Case of Finitely Many Isolated Singularities
4.2 Embedded Complete Definite Improper Affine Map with a Planar Singular Set
References
Affine Isoperimetric Inequalities for Lp Geominimal Surface Area
1 Introduction
2 Notation and Definitions
3 Lp Geominimal Surface Area
4 An Affine Isoperimetric Inequality Between Gp and Op
5 Lp Mixed Geominimal Surface Area
References
Real Hypersurfaces in Complex Two-Plane Grassmannians with Commuting Jacobi Operators
1 Introduction
2 Proof of Theorem 4
3 Proof of Theorem 5
References
Parallelism on Jacobi Operators for Hopf Hypersurfaces in Complex Two-Plane Grassmannians
1 Introduction
2 Proof of Theorem 2
3 Proof of Theorem 3
4 Proof of Theorem 4
References
The *-Ricci Tensor of Real Hypersurfaces in Symmetric Spaces of Rank One or Two
1 Introduction
2 Real Hypersurfaces in Complex Space Forms
2.1 Three Dimensional Real Hypersurfaces in CP2 or CH2
3 Conditions of Parallelness of *-Ricci Tensor of Real Hypesurfaces in Complex Space Forms
3.1 Real Hypersurfaces in M2(c) with Parallel *-Ricci Tensor
3.2 Real Hypersurfaces in M2(c) with Semi-Parallel *-Ricci Tensor
3.3 Real Hypersurfaces in M2(c) with Pseudo-Parallel *-Ricci Tensor
4 *-Ricci Tensor of Real Hypersurfaces in G2(Cm+2)
References
On Totally Geodesic Surfaces in Symmetric Spaces of Type AI
1 Introduction
2 Preliminaries
2.1 General Preliminaries
2.2 Preliminaries for Type AI
3 Main Theorem
4 Some Explicit Classifications
4.1 The Case of n=3
4.2 The Case of n=4
References
Examples of Non-Kähler Solvmanifolds AdmittingHodge Decomposition
1 Introduction
1.1 Nakamura Manifolds
1.2 Nakamura-Like Manifolds
2 Kähler Geometry
2.1 Formality
2.2 Hard Lefschetz Property
2.3 Hodge Decomposition
3 Cohomologies of Solvmanifolds
3.1 Cohomology of Nilmanifolds
3.2 de Rham Cohomology of Solvmanifolds
3.3 Dolbeault and Bott-Chern cohomologies of Splitting Solvmanifolds
3.4 Dolbeault and Bott-Chern Cohomologies of Complex Parallelizable Solvmanifolds
4 Hodge Theory on Solvmanifolds
5 Computations on Nakamura Manifolds and Nakamura-Like Manifolds
5.1 Nakamura Manifolds
5.2 Nakamura-Like Manifolds
References
Some Characterizations of Real Hypersurfaces in Complex Hyperbolic Two-Plane Grassmannians
1 Introduction
2 Complex Hyperbolic Two-Plane Grassmannians
3 Real Hypersurfaces in SU2,m/S(U2·Um)
4 Proof of Theorem 2
5 Proof of Corollaries
References
Heat Content Asymptotics on a Compact Riemannian Manifold with Boundary
1 Introduction
1.1 Definitions and Notation
1.2 The Heat Equation and the Heat Content
2 Asymptotic Series of Heat Content
2.1 Heat Content Asymptotics for Dirichlet Boundary Conditions
2.2 Heat Content Asymptotics for Robin Boundary Conditions
3 Existence of Heat Content Asymptotic Series
References
Real Hypersurfaces in Complex Two-Plane Grassmannians with Recurrent Structure Jacobi Operator
1 Introduction
2 Riemannian Geometry of G2(Cm+2)
3 Some Fundamental Formulas for Real Hypersurfaces in G2(Cm+2)
4 The D-recurrent Structure Jacobi Operator
5 Proof of the Main Theorem
References
The Warped Product Approach to GMGHS Spacetime
1 Introduction
2 Magnetically Charged GMGHS Black Hole in the Framework of Warped Products
3 Geodesic Motion Near a Hypersurface with C0-warping Function
References
Reeb Flow Invariant Ricci Tensors
1 Introduction
2 Preliminaries
3 Reeb Flow Symmetries on Contact Three-Manifolds
4 Lie Groups and Examples
References
Totally Geodesic Surfaces of Riemannian Symmetric Spaces
1 Introduction
2 Irreducible Representation of SU(2)
2.1 Complex Irreducible Representations
2.2 Real Irreducible Representations
3 Classification
3.1 AI: SU(n)/SO(n)
3.2 AIII: SU(p+q)/S(U(p)U(q))
3.3 BDI: SO(p+q)/S(O(p)O(q))
References
The Geometry on Hyper-Kähler Manifolds of Type A8
1 Introduction
2 Hyper-Kähler Manifolds of Type A8
2.1 Hyper-Kähler Quotient Construction
2.2 S1-actions and Moment Maps
3 The Volume Growth
4 Period Maps
4.1 Holomorphic Curves
4.2 Topology
4.3 Period Maps
5 Holomorphic Symplectic Structures
References
The Fixed Point Set of a Holomorphic Isometry and the Intersection of Two Real Forms in the Complex Grassmann Manifold
1 Introduction
2 The Fixed Point Set of a Holomorphic Isometry of the Complex Grassmann Manifold
3 The Intersection of Two Real Grassmann Manifolds in the Complex Grassmann Manifold
4 The Intersection and the Fixed Point Set
5 Further Results
References
Canonical Forms Under Certain Actions on the Classical Compact Simple Lie Groups
1 s-actions
2 s-actions and Symmetric Triads
2.1 General Case
2.2 In the Case When s Is of Finite Order
2.3 In the Case When s2=1
References
Elementary Deformations and the HyperKähler-Quaternionic Kähler Correspondence
1 Introduction
2 Twist Constructions
3 Elementary Deformations of HyperKähler Metrics
4 The HyperKähler-Quaternionic Kähler Correspondence
5 Application to the c-map
References
A Classification of Ricci Solitons as (k,µ)-Contact Metrics
1 Introduction
2 Preliminaries
3 Proof of Theorem 1
4 An Example of the Last Case of Theorem 1
References
Real Hypersurfaces in Kähler Manifolds
1 Introduction
2 Real Hypersurfaces of Kähler Manifolds
3 Contact Manifolds as Real Hypersurfaces in Complex Projective Spaces
4 Cosymplectic Manifolds as Real Hypersurfaces in Kähler Manifolds
References
Lp-Spectral Gap and Gromov-Hausdorff Convergence
1 Introduction
2 Key Steps
3 Applications
References
Riemannian Questions with a Fundamental Differential System
1 Geometric Structures and the Fundamental Differential System
1.1 The Manifold SM
1.2 Further Metric Properties
1.3 The Contact Structure
1.4 Some Structural Relations
1.5 Gwistor Space and Problems for Calibrated Geometries
2 Geometric Applications
2.1 Recalling Euler-Lagrange Systems
2.2 On the Unit Tangent Sphere Bundle
References
Lagrangian Intersection Theory and Hamiltonian Volume Minimizing Problem
1 Introduction
2 Antipodal Sets of Complex Flag Manifolds
3 The Intersection of Real Flag Manifolds in a Complex Flag Manifold
4 Application to the Hamiltonian Volume Minimizing Problem
References
An SL2(C) Topological Invariant of Knots
1 Introduction
2 SL2(C) Algebro-Geometric Invariant of Knots
3 An SL2(C) Casson Type Topological Invariant of Hyperbolic Knots
References
The Möbius Geometry of Wintgen Ideal Submanifolds
1 Introduction
2 Submanifold Theory in Möbius Geometry
3 Invariants of a Wintgen Ideal Submanifold
4 The Conformal Gauss Map as a Harmonic Map
5 The Spherical Foliation Structure
6 Special Classes of Wintgen Ideal Submanifolds
References
Floer Homology for the Gelfand-Cetlin System
1 Introduction
2 Gelfand-Cetlin System
3 Potential Functions for Gelfand-Cetlin Systems
4 Floer Homologies of Non-torus Fibers
4.1 Floer Homology of Lagrangian S3 in Fl(3)
4.2 Floer Homologies of U(2)-fibers in Gr(2,4)
References
The Regularized Mean Curvature Flow for Invariant Hypersurfaces in a Hilbert Space
1 Introduction
2 The Regularized Mean Curvature Flow
3 The Mean Curvature Flow in Riemannian Orbifolds
4 Evolution Equations
5 Horizontally Strongly Convexity Preservability Theorem
6 Strongly Convex Preservability Theorem in the Orbit Space
References
Harmonic Maps into Grassmannians
1 Introduction
2 Preliminaries
2.1 A Harmonic Map
2.2 Geometry of Grassmannians
3 Harmonic Maps into Grassmannians
4 A Generalization of Theory of Do Carmo and Wallach
4.1 Standard Maps
4.2 A Generalization of Do Carmo-Wallach Theory
5 Harmonic Maps into Complex Projective Spaces
6 Holomorphic Isometric Embeddings of the Projective Line into Quadrics
References
Conformal Transformations Between Complete Product Riemannian Manifolds
1 Introduction
2 Theorems and an Example
3 Almost Product Riemannian Structure and Separate Coordinate System
4 Proof of Theorem 1
5 Proof of Theorem 2
References
Orbifold Holomorphic Discs and Crepant Resolutions
1 Holomorphic Discs
2 Orbi-Discs
3 Lagrangian Floer Superpotential and CrepantResolutions
References
On the Hamiltonian Minimality of Normal Bundles
1 Introduction
2 Hamiltonian Minimal Lagrangian Submanifolds
3 Hamiltonian Minimality of Normal Bundles in TRn+k
3.1 H-Minimal Lagrangian Submanifolds in Cm
3.2 Normal Bundles in TRn+k
3.3 Normal Bundles over Isoparametric Submanifolds
3.4 Outline of a Proof of Theorem 1
References
Construction of Coassociative Submanifolds
1 Introduction
2 Construction of Examples with Symmetries
3 Coassociative Submanifolds in R7
3.1 The Case G = SU(2)
3.2 The Case G = T2 R&0
4 Coassociative Submanifolds in ?2- S4
4.1 G2-Structure on ?2- S4
4.2 The Case G = SU(2)
4.3 The Case G = T2 R&0
References
Calibrations and Manifolds with Special Holonomy
1 Introduction
2 Basic Definitions
3 Calabi-Yau's Hypersurfaces in G2 Manifolds
4 HL Manifolds and Mirror Duality in G2 Manifolds
References
Sequences of Maximal Antipodal Sets of Oriented Real Grassmann Manifolds
1 Introduction
2 Antipodal Subsets
3 Combinatorial Sequences of Antipodal Subsets
4 Even Sequences of Antipodal Subsets
References
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Real and Complex Submanifolds

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