Structures on Manifolds

Title Page......Page 1
Copyright Page......Page 2
Preface......Page 3
Contents......Page 5
1. Manifolds and tensor fields......Page 9
2. Connections and covariant differentiations......Page 26
3. Sectional curvature......Page 39
4. Transformations......Page 48
5. Fibre bundles and covering spaces......Page 54
Exercises......Page 62
1. Induced connection and second fundamental form......Page 69
2. Equations of Gauss, Codazzi and Ricci......Page 75
3. Laplacian of the second fundamental form......Page 81
4. Submanifolds of space forms......Page 86
5. Minimal sutxnanifolds......Page 97
Exercises......Page 107
1. Almost complex manifolds and complex manifolds......Page 112
2. Examples of complex manifolds and almost complex manifolds......Page 126
3. Hermitian manifolds......Page 132
4. Kaehlerian manifolds......Page 137
5. Nearly Kaehlerian manifolds......Page 152
6. Quaternion Kaehlerian manifolds......Page 166
Exercises......Page 182
CHAPTER IV SUBMANIFOLDS OF KAEHLERIAN MANIFOLDS......Page 187
1. Kaehlerian submanifolds......Page 188
2. Anti-invariant submanifolds of Kaehlerian manifolds......Page 207
3. CR submanifolds of Kaehlerian manifolds......Page 222
Exercises......Page 252
CHAPTER V CONTACT MANIFOLDS......Page 259
1. Almost contact manifolds......Page 260
2. Contact manifolds......Page 263
3. Torsion tensor of almost contact manifolds......Page 271
4. Contact distribution......Page 277
5. Sasakian manifolds......Page 280
6. Regular contact manifolds......Page 294
7. Brieskorn manifolds......Page 299
Exercises......Page 314
CHAPTER VI SUBMANIFOLDS OF SASAKIAN MANIFOLDS......Page 319
1. Invariant submanifolds of Sasakian manifolds......Page 320
2. Anti-invariant submanifolds tangent to the structure vector field of Sasakian manifolds......Page 337
3. Anti-invariant submanifolds normal to the structure vector field of Sasakian manifolds......Page 352
4. Contact CR submanifolds......Page 359
5. Induced structures on submanifolds......Page 374
Exercises......Page 380
1. f-structure on manifolds......Page 387
2. Normal f-structure......Page 400
3. Framed f-structure......Page 410
4. Hypersurfaces of framed manifolds......Page 416
Exercises......Page 420
1. Locally product manifolds......Page 422
2. Locally decomposable Riemannian manifolds......Page 426
3. Sutmanifolds of product manifolds......Page 432
4. Submanifolds of Kaehlerian product manifolds......Page 437
Exercises......Page 444
1. Fundamental equations of submersions......Page 447
2. Almost Hermitian sutmersions......Page 456
3. Submersions and sutmanifolds......Page 463
Exercises......Page 475
BIBLIOGRAPHY......Page 481
INDEX......Page 503