Differential and Riemannian Manifolds [[electronic resource] /] / by Serge Lang

• Record Nr.: UNINA9910480453003321
• Autore: Lang Serge
• Pubbl/distr/stampa: New York, NY : , : Springer New York : , : Imprint : Springer, , 1995
• ISBN: 1-4612-4182-0
• Edizione: [3rd ed. 1995.]
• Descrizione fisica: 1 online resource (XIV, 364 p.)
• Collana: Graduate Texts in Mathematics, , 0072-5285 ; ; 160
• Disciplina: 516.36
• Soggetti: Differential geometry; Mathematical analysis; Analysis (Mathematics); Algebraic topology; Differential Geometry; Analysis; Algebraic Topology
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "With 20 Illustrations."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: I Differential Calculus -- §1. Categories -- §2. Topological Vector Spaces -- §3. Derivatives and Composition of Maps -- §4. Integration and Taylor’s Formula -- §5. The Inverse Mapping Theorem -- II Manifolds -- §1. Atlases, Charts, Morphisms -- §2. Submanifolds, Immersions, Submersions -- §3. Partitions of Unity -- §4. Manifolds with Boundary -- III Vector Bundles -- §1. Definition, Pull Backs -- §2. The Tangent Bundle -- §3. Exact Sequences of Bundles -- §4. Operations on Vector Bundles -- §5. Splitting of Vector Bundles -- IV Vector Fields and Differential Equations -- §1. Existence Theorem for Differential Equations -- §2. Vector Fields, Curves, and Flows -- §3. Sprays -- §4. The Flow of a Spray and the Exponential Map -- §5. Existence of Tubular Neighborhoods -- §6. Uniqueness of Tubular Neighborhoods -- V Operations on Vector Fields and Differential Forms -- §1. Vector Fields, Differential Operators, Brackets -- §2. Lie Derivative -- $3. Exterior Derivative -- §4. The Poincaré Lemma -- §5. Contractions and Lie Derivative -- §6. Vector Fields and 1-Forms Under Self Duality -- §7. The Canonical 2-Form -- §8. Darboux’s Theorem -- ; VI The Theorem of Frobenius -- §1. Statement of the Theorem -- §2. Differential Equations Depending on a Parameter -- §3. Proof of the Theorem -- §4. The Global Formulation -- §5. Lie Groups and Subgroups -- VII Metrics -- §1. Definition and Functoriality -- §2. The Hilbert Group -- §3. Reduction to the Hilbert Group -- §4. Hilbertian Tubular Neighborhoods -- §5. The Morse—Palais Lemma -- §6. The Riemannian Distance -- §7. The Canonical Spray -- VIII Covariant Derivatives and Geodesics -- §1. Basic Properties -- §2. Sprays and Covariant Derivatives -- §3. Derivative Along a Curve and Parallelism -- §4. The Metric Derivative -- §5. More Local Results on the Exponential Map -- §6. Riemannian Geodesic Length and Completeness -- IX Curvature -- §1. The Riemann Tensor -- §2. Jacobi Lifts -- §3. Application of Jacobi Lifts to dexpx -- §4. The Index Form, Variations, and the Second Variation Formula -- §5. Taylor Expansions -- X Volume Forms -- §1. The Riemannian Volume Form -- §2. Covariant Derivatives -- §3. The Jacobian Determinant of the Exponential Map -- §4. The Hodge Star on Forms -- §5. Hodge Decomposition of Differential Forms -- XI Integration of Differential Forms -- §1. Sets of Measure 0 -- §2. Change of Variables Formula -- §3. Orientation -- §4. The Measure Associated with a Differential Form -- XII Stokes’ Theorem -- §1. Stokes’ Theorem for a Rectangular Simplex -- §2. Stokes’ Theorem on a Manifold -- §3. Stokes’ Theorem with Singularities -- XIII Applications of Stokes’ Theorem -- §1. The Maximal de Rham Cohomology -- §2. Moser’s Theorem -- §3. The Divergence Theorem -- §4. The Adjoint of d for Higher Degree Forms -- §5. Cauchy’s Theorem -- §6. The Residue Theorem -- Appendix The Spectral Theorem -- §1. Hilbert Space -- §2. Functionals and Operators -- §3. Hermitian Operators.
• Sommario/riassunto: This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.).

The mind of the chimpanzee : ecological and experimental perspectives / / Elizabeth V. Lonsdorf, Stephen R. Ross, & Tetsuro Matsuzawa

• Record Nr.: UNINA9910972266303321
• Autore: Lonsdorf Elizabeth
• Pubbl/distr/stampa: Chicago, : University of Chicago Press, c2010
• ISBN: 9786612710735; 9781282710733; 1282710737; 9780226492810; 0226492818
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (393 p.)
• Altri autori (Persone): RossStephen R; MatsuzawaTetsurō <1950->; GoodallJane <1934-2025.>
• Disciplina: 599.885/15
• Soggetti: Chimpanzees - Behavior; Chimpanzees - Psychology; Chimpanzees - Ecology; Chimpanzees - Conservation; Cognition in animals; Social behavior in animals
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Front matter -- Contents -- Foreword -- Acknowledgments -- 1. The Chimpanzee Mind: Bridging Fieldwork and Laboratory Work -- 2. Early Social Cognition in Chimpanzees -- 3. Using an Object Manipulation Task as a Scale for Comparing Cognitive Development in Chimpanzees and Humans -- 4. Do the Chimpanzee Eyes Have It? -- 5. Understanding the Expression and Classification of Chimpanzee Facial Expressions -- 6. Behavioral and Brain Asymmetries in Chimpanzees -- 7. Trapping the Minds of Apes: Causal Knowledge and Inferential Reasoning about Object-Object Interactions -- 8. A Coming of Age for Cultural Panthropology -- 9. The Cultural Mind of Chimpanzees: How Social Tolerance Can Shape the Transmission of Culture -- 10. How Are ; Army Ants Shedding New Light on Culture in Chimpanzees? -- 11. The Complexity of Chimpanzee Tool-Use Behaviors -- 12. Tools, Traditions, and Technologies: Interdisciplinary Approaches to Chimpanzee Nut Cracking -- 13. Ubiquity of Culture and Possible Social Inheritance of Sociality among Wild Chimpanzees -- 14. New Theaters of Conflict in the Animal Culture Wars: Recent Findings from Chimpanzees -- 15. Chimpanzee Minds in Nature -- 16. Vocal Communication in Chimpanzees -- 17. The Function and Cognitive Underpinnings of Post-Conflict Affiliation in Wild Chimpanzees -- 18. The Role of Intelligence in Group Hunting: Are Chimpanzees Different from Other Social Predators? -- 19. Chimpanzee Social Cognition -- 20. Intentional Communication and Comprehension of the Partner's Role in Experimental Cooperative Tasks -- 21. Collaboration and Helping in Chimpanzees -- 22. Inequity and Prosocial Behavior in Chimpanzees -- 23. The Need for a Bottom-Up Approach to Chimpanzee Cognition -- 24. How Cognitive Studies Help Shape Our Obligation for the Ethical Care of Chimpanzees -- 25. Positive Reinforcement Training, Social Learning, and Chimpanzee Welfare -- 26. Chimpanzee Orphans: Sanctuaries, Reintroduction, and Cognition -- 27. Human-Chimpanzee Competition and Conflict in Africa: A Case Study of Coexistence in Bossou, Republic of Guinea -- 28. Chimpanzee Mind, Behavior, and Conservation -- Afterword: Meanings of Chimpanzee Mind -- Appendix: Major Chimpanzee Research Sites -- Index
• Sommario/riassunto: Understanding the chimpanzee mind is akin to opening a window onto human consciousness. Many of our complex cognitive processes have origins that can be seen in the way that chimpanzees think, learn, and behave. The Mind of the Chimpanzee brings together scores of prominent scientists from around the world to share the most recent research into what goes on inside the mind of our closest living relative. Intertwining a range of topics-including imitation, tool use, face recognition, culture, cooperation, and reconciliation-with critical commentaries on conservation and welfare, the collection aims to understand how chimpanzees learn, think, and feel, so that researchers can not only gain insight into the origins of human cognition, but also crystallize collective efforts to protect wild chimpanzee populations and ensure appropriate care in captive settings. With a breadth of material on cognition and culture from the lab and the field, The Mind of the Chimpanzee is a first-rate synthesis of contemporary studies of these fascinating mammals that will appeal to all those interested in animal minds and what we can learn from them.