Structures On ManifoldsWorld Scientific, Feb 1, 1985 - 520 pages Contents: Riemannian ManifoldsSubmanifolds of Riemannian ManifoldsComplex ManifoldsSubmanifolds of Kaehlerian ManifoldsContact ManifoldsSubmanifolds of Sasakian Manifoldsf-StructuresProduct ManifoldsSubmersions Readership: Mathematicians. Keywords:Riemannian Manifold;Submanifold;Complex Manifold;Contact Manifold;Kaehlerian Manifold;Sasakian Manifold;Anti-Invariant Submanifold;CR Submanifold;Contact CR Submanifold;Submersion |
Contents
| 1 | |
CHAPTER II SUBMANIFOLDS OF RIEMANNIAN MANIFOLDS | 61 |
CHAPTER III COMPLEX MANIFOLDS | 104 |
CHAPTER IV SUBMANIFOLDS OF KAEHLERIAN MANIFOLDS | 179 |
CHAPTER V CONTACT MANIFOLDS | 251 |
CHAPTER VI SUBMANIFOLDS OF SASAKIAN MANIFOLDS | 311 |
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2n+1)-dimensional algebra anti-invariant submanifold called codimension complex manifold complex projective space complex space form complex structure components constant curvature constant holomorphic sectional contact manifold contact structure coordinate system covariant CR submanifold curvature tensor curvature vector defined denote Differential Geometry dimension equation f-structure flat normal connection following THEOREM framed manifold hence Hermitian holomorphic sectional curvature implies invariant submanifold isometric immersion K-contact Kaehlerian submanifold Lemma linear mapping mean curvature mean curvature vector metric g minimal submanifold Moreover nearly Kaehlerian manifold normal bundle obtain orthogonal orthonormal basis product manifold Proof PROPOSITION proved the following resp respect Ricci tensor Riemannian curvature tensor Riemannian manifold Riemannian metric Sasakian manifold Sasakian space form Sasakian structure satisfies scalar curvature second fundamental form sectional curvature structure vector field submani submersion symmetric tangent space tensor field totally geodesic vanishes