{"product_id":"classical-and-discrete-differential-geometry-9781032390178","title":"Classical and Discrete Differential Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book introduces differential geometry and cutting-edge findings from the discipline by incorporating both classical approaches and modern discrete differential geometry across all facets and applications, including graphics and imaging, physics and networks.\u003c\/p\u003e\u003cp\u003eWith curvature as the centerpiece, the authors present the development of differential geometry, from curves to surfaces, thence to higher dimensional manifolds; and from smooth structures to metric spaces, weighted manifolds and complexes, and to images, meshes and networks. The first part of the book is a differential geometric study of curves and surfaces in the Euclidean space, enhanced while the second part deals with higher dimensional manifolds centering on curvature by exploring the various ways of extending it to higher dimensional objects and more general structures and how to return to lower dimensional constructs. The third part focuses on computational algorithms in algebraic topology and conformal geometry, applicable for surface parameterization, shape registration and structured mesh generation.\u003c\/p\u003e\u003cp\u003eThe volume will be a useful reference for students of mathematics and computer science, as well as researchers and engineering professionals who are interested in graphics and imaging, complex networks, differential geometry and curvature.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eSection I Differential Geometry, Classical and Discrete\u003c\/strong\u003e 1. Curves 2. Surfaces: Gauss Curvature – First Definition 3. Metrization of Gauss Curvature 4. Gauss Curvature and Theorema Egregium 5. The Mean and Gauss Curvature Flows 6. Geodesics 7. Geodesics and Curvature 8. The Equations of Compatibility 9. The Gauss-Bonnet Theorem and the Poincare Index Theorem 10. Higher Dimensional Curvatures 11. Higher Dimensional Curvatures 12. Discrete Ricci Curvature and Flow 13. Weighted Manifolds and Ricci Curvature Revisited \u003cstrong\u003eSection II Differential Geometry, Computational Aspects \u003c\/strong\u003e 14. Algebraic Topology 15. Homology and Cohomology Group 16. Exterior Calculus and Hodge Decomposition 17. Harmonic Map 18. Riemann Surface 19. Conformal Mapping 20. Discrete Surface Curvature Flows 21. Mesh Generation Based on Abel-Jacobi Theorem \u003cstrong\u003eSection III Appendices\u003c\/strong\u003e 22. Appendix A 23. Appendix B 24. Appendix C\u003c\/p\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":52084468482391,"sku":"9781032390178","price":95.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781032390178.jpg?v=1762206471","url":"https:\/\/bookcurl.com\/products\/classical-and-discrete-differential-geometry-9781032390178","provider":"Book Curl","version":"1.0","type":"link"}