Tensor Operators and their Applications.

Intro -- TENSOR OPERATORS AND THEIR APPLICATIONS -- LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA -- Contents -- Preface -- Chapter 1 On Operators Applied to Pure Tensor Fields -- 1.1. Pure Tensor Fields -- 1.2. Tachibana Operators -- 1.2.1. φϕ−operator Applied to a Tensor Field of Type (1,1) -- 1.2.2. φϕ−operator Applied to a Tensor Field of Type (1,s), s≥2 -- 1.2.3. φϕ−operator Applied to a 1-form -- 1.2.4. φϕ−operator Applied to a Tensor Field of Type (0,s), s≥2 -- 1.2.5. φϕ−operator Applied to a Tensor Field of Type (r,s) -- 1.3. Vishnevskii Operators -- 1.3.1. ψϕϕ−operator Applied to a Tensor Field of Type (1,s), s≥0 -- 1.3.2. ψϕ−operator Applied to a Tensor Field of Type (0,s) -- 1.3.3. ψϕ−operator Applied to a Tensor Field of Type (r,s), r&gt -- 1 -- 1.4. ψϕ−operator Applied to a Pure Connection -- 1.5. Tachibana Operators Applied to a Mixed Tensor Field -- 1.5.1. Pure Tensor Fields of Mixed Kindon Submanifolds -- 1.5.2. φϕ,ϕ−operators -- 1.5.3. φ−operator Applied to Tensor Fields of Type (1,s,0,q) and (0,s,1,q) -- 1.5.4. ϕφ,φ−operator Applied to Tensor Fields of Type (0,s,0,0) and (0,0,0,q) -- 1.6. Yano-Ako Operators -- 1.6.1. De nitions -- 1.6.2. ϕS−operator Applied to a Tensor Field of Type (1,s) -- 1.6.3. ϕS−operator Applied to a Tensor Field of Type (0,s) -- 1.7. ψs−operators -- 1.7.1. ψS−operator Applied to a Tensor Field of Type (1,s), s≥0 -- 1.7.2. ψS−operator Applied to a Tensor Field of Type (0,s) -- 1.8. Generalizations -- Chapter 2 Algebraic Structures on Manifolds -- 2.1. Algebraic Theory -- 2.1.1. Associative Algebras -- 2.1.2. Commutative Algebras -- 2.1.3. Holomorphic Functions -- 2.2. Algebraic Π−structures on Manifolds -- 2.3. Integrable Regular Π−structure -- 2.4. Pure Tensors with Respect to the Regular Structure -- 2.5. A-holomorphic Tensors in Real Coordinate Systems -- 2.6. Pure Connections.

2.7. Torsion Tensors of Pure Π−connections -- 2.8. A−holomorphic Hypercomplex Connection -- 2.9. Some Properties of Pure Curvature Tensors -- Chapter 3 Applications to the Norden Geometry -- 3.1. Hyper-Kahler-Norden Manifolds -- 3.2. Complex Kahler-Norden Manifolds -- 3.3. Almost Product Riemannian Manifolds -- 3.3.1. Decomposable Riemannian Manifolds -- 3.3.2. Para-Kahler-Norden Manifolds -- 3.3.3. Nonexistence of Para-Kahler-Norden Warped Metrics -- 3.4. Dual-Kahler-Norden Manifolds -- 3.5. Norden-Hessian Structures -- 3.6. Norden-Walker Manifolds with Proper Structures -- 3.6.1. Almost Norden-Walker Metrics -- 3.6.2. Integrability of Proper Almost Complex Structures -- 3.6.3. Holomorphic Norden-Walker (Kahler-Norden-Walker) Metrics -- 3.6.4. Curvature Properties of Norden-Walker Manifolds -- 3.6.5. Isotropic Kahler-Norden-Walker Structures -- 3.6.6. Quasi-Kahler-Norden-Walker Structures -- 3.6.7. On the Goldberg Conjecture -- 3.7. Opposite Almost Complex Structure -- 3.8. Para-Norden-Walker Metrics -- 3.9. Some Notes Concerning Norden-Walker 8-manifolds -- Chapter 4 Applications to the Theory of Lifts -- 4.1. Tensor Bundles -- 4.2. Horizontal and Complete Lifts of Vector Fields -- 4.2.1. Vertical Lifts of Tensor Fields and γ−operator -- 4.2.2. Complete Lifts of Vector Fields -- 4.2.3. Horizontal Lifts of Vector Fields -- 4.2.4. Complete Lifts of Derivations -- 4.2.5. Derivations DKXY1 and Formulas on Lie Derivations -- 4.3. Cross-sections in the Tensor Bundle -- 4.4. Lifts of Af nor Fields -- 4.4.1. Complete Lifts of Af nor Fields -- 4.4.2. Almost Complex Structures on Tqp(Mn) -- 4.4.3. Almost Hyperholomorphic Pure Submanifolds in the Tensor Bundle -- 4.4.4. Horizontal Lifts of Af nor Fields -- 4.4.5. Diagonal Lifts of Af nor Fields -- 4.5. Lifts of Metrics -- 4.5.1. Adapted Frames -- 4.5.2. Sasakian Metrics on the Tensor Bundles.

4.5.3. Geodesics on Tensor Bundles -- 4.5.4. Jacobi Tensor Fields -- 4.6. Some Special Cases -- 4.6.1. Para-Nordenian Structures in Cotangent Bundles -- 4.6.2. Paraholomorphic Cheeger-Gromoll Metric in the Tangent Bundle -- 4.6.3. On Almost Complex Structures in Tangent Bundles -- 4.7. Complete Lift of a Skew-Symmetric Tensor Field -- References -- Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.