Ebook: CR Submanifolds of Kaehlerian and Sasakian Manifolds

This volume presents an introduction and survey of
the latest results pertaining to the study of CR sub.
manifolds of Kaehlerian and Sasakian manifolds, a
relatively new field of differential geometry. The
volume also contains all prerequisite information on
Riemannian, Kaehlerian, Sasakian manifolds, f-struc-
tures, and submaitifolds necessary to understand these
results.


Introduction

Chapter I. Structures on Riemannian manifolds
91. Riemannian manifolds
92. Kaehlerian manifolds
93. Sasakiilll milllifolds
94. f-structure

Chapter II. Submanifolds
91. Induced connection illld second fundamental form
92. Equations of Gauss, Codazzi illld Ricci
93. Normal connection
94. Laplacian of the second fundamental form
95. Subnillllifolds of space forms
96. Parallel second fundamental form

Chapter III. Contact CR submanifolds
91. Submanifolds of Sasakian manifolds
92. f-structure on submanifolds
93. Integrability of distributions
94. Totally contact umbilical submanifolds
95. EXillnplcs of contact CR submilllifolds
96. Flat normal connection
97. minimal contact CR submanifolds

Chapter IV. CR submanifolds
91. Submanifolds of Kaehlerian manifolds
92. CR submanifolds of IIermitian manifolds
93. Characterization of CR submanifolds
94. Distributions
95. Parallel f-structure
96. Totally umbilical submanifolds
97. Examples of CR submanifolds
98. Semi-flat normal connection
99. Normal connection of invariant submanifolds
910. Parallcl mean curvature vector
911. Integral fonnulas

912. CR submanifolds of em

Chapter V. Submanifolds and Riemannian fibre bundles
91. Curvature tensors
92. Mean curvature vector
93. Lengths of the second fundamental forms

Chapter VI. Hypersurfaces
Real hypersurfaces of complex space forms
Pseudo-Einstein real hypersurfaces
Generic minimal submanifolds
Semidefinite second fundamental form
Hypersurfaces of S2n+l
(f,g,u,V,A)-structure

Bibliography
Author index
Subject index