This book introduces a number of ideas in differential geometry centred around recent work on isoparametric submanifolds. After an initial introduction to the geometry of submanifolds, the author discusses the idea of focal points and principal curvatures. The topic is treated from a totally new geometric point of view where the geometry of the set of critical normals is taken as a way of discussing relations between the principal curvatures. Recent work on holonomy group of the normal bundle of a submanifold due to Thorbergsson, Olmos, Heintze and others are described. The examples of isoparametric submanifolds due to Ferus, Karcher and Munzner is considered in some detail.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Maße
ISBN-13
978-981-02-0771-7 (9789810207717)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Klassifikation
Submanifolds of IR to the power of n; tangent fields; normal fields; covariant differentiation; Gauss-Codazzi equations; parallel submanifolds in IR to the power of n; relations between the shape operators; holonomy groups; normal holonomy groups; manifolds with flat normal bundle; isoparametric systems and their basic properties; an homogeneous example; isotropy representations; the Ferus-Karcher-Munzner examples; focal manifolds of isoparametric systems; Strubing's condition; Tits buildings and isoparametric submanifolds.
