Geometry of submanifolds and its applications

CONTENTS......Page 3
Preface......Page 5
1. Riemannian manifolds.   ......Page 7
2. Submanifolds ......Page 8
3. Submanifolds with planar normal sections ......Page 9
4. The first and second variations of volume- ......Page 14
1. Introduction  ......Page 16
3. Surfaces with parallel normalized mean curvature vector ......Page 17
1. Rotation index, regular homotopy and total curvature ......Page 21
2. Total mean curvature  ......Page 22
3. Total mean curvature and conformal geometry......Page 23
4. Total mean curvature, order of immersion, and spectral geometry - ......Page 26
5. Total mean curvature and topology  ......Page 31
6. Remarks and Conjectures ......Page 33
1. Differentiabilities and Openness.   ......Page 36
2. Integrabilities ......Page 38
3. Generic submanifolds of complex-space-forms ......Page 40
4. Generic products  ......Page 42
5. Application to complex geometry ......Page 46
1. Integrability, minimality and cohomology ......Page 47
2. CR-products of Kaehier manifolds ......Page 50
4. Stability of totally real submanifolds ......Page 55
1. Totally geodesic submanifolds and (^+,M_)-method ......Page 58
2. General theory  ......Page 59
3. Determination of the pairs ......Page 63
4. Applications  ......Page 66
1. Fixed point sets and twisted products   ......Page 70
2. Reducible totally umbilical submanifolds     ......Page 73
3. Codimension of totally umbilical submanifolds  ......Page 74
4. Totally umbilical hypersurfaces   ......Page 76
5. Irreducible totally umbilical submanifolds   ......Page 80
6. Totally umbilical submaniflods of Kaehler maniflds   ......Page 81
7. Extrinsic spheres of Kaehler manifolds     ......Page 86
Bibliography ......Page 90
Subject Index     ......Page 99