Category: Differential Geometry

By Mikhail Itskov

This is the fourth and revised variation of a well-received e-book that goals at bridging the distance among the engineering process tensor algebra at the one aspect and the mathematical process classical linear algebra at the different facet. in response to the modern method of clinical guides, a contemporary absolute tensor notation is most popular all through. The e-book presents a understandable exposition of the elemental mathematical techniques of tensor calculus and enriches the offered fabric with many illustrative examples. additionally, the e-book additionally contains complex chapters facing contemporary advancements within the conception of isotropic and anisotropic tensor features and their purposes to continuum mechanics. as a result, this monograph addresses graduate scholars in addition to scientists operating during this box. In each one bankruptcy a variety of workouts are incorporated, taking into consideration self-study and extreme perform. suggestions to the routines also are provided.

By Sorin Dragomir

A very good reference for someone desiring to ascertain homes of harmonic vector fields to assist them resolve examine difficulties. The e-book offers the most result of harmonic vector fields with an emphasis on Riemannian manifolds utilizing previous and current difficulties to help you in examining and furnishing your personal end for additional learn. It emphasizes a mixture of theoretical improvement with useful functions for a great therapy of the topic helpful to these new to analyze utilizing differential geometric equipment in wide detail.A great tool for any scientist undertaking examine within the box of harmonic analysisProvides functions and smooth concepts to challenge fixing a transparent and concise exposition of differential geometry of harmonic vector fields on Reimannian manifoldsPhysical functions of Geometric equipment

By S. K. Donaldson

The final ten years have noticeable swift advances within the realizing of differentiable four-manifolds, now not least of which has been the invention of recent 'exotic' manifolds. those effects have had far-reaching effects in geometry, topology, and mathematical physics, and feature confirmed to be a mainspring of present mathematical learn. This ebook presents a lucid and available account of the fashionable examine of the geometry of four-manifolds. for this reason, it will likely be required studying for all these mathematicians and theoretical physicists whose study touches in this subject. The authors current either a radical remedy of the most traces of those advancements in four-manifold topology--notably the definition of latest invariants of four-manifolds--and additionally a wide-ranging remedy of correct subject matters from geometry and worldwide research. the entire major theorems approximately Yang-Mills instantons on four-manifolds are confirmed intimately. at the geometric facet, the ebook incorporates a new evidence of the type of instantons at the four-sphere, including an in depth dialogue of the differential geometry of holomorphic vector bundles. on the finish of the booklet the various strands of the speculation are introduced jointly within the proofs of effects which settle long-standing difficulties in four-manifolds topology and that are just about the frontiers of present examine. Co-author Donaldson is the 1994 co-recipient of the distinguished Crafoord Prize.

By Y Matsushima

Some time past 30 years, differential geometry has passed through a big swap with infusion of topology, Lie idea, advanced research, algebraic geometry and partial differential equations. Professor Matsushima performed a number one position during this transformation through bringing new thoughts of Lie teams and Lie algebras into the examine of actual and intricate manifolds. This quantity is a set of all of the forty six papers written by means of him.

By Paulette Libermann

Approach your difficulties from the ideal finish it's not that they can not see the answer. and start with the solutions. Then at some point, it really is that they can not see the matter. probably you can find the ultimate query. G. okay. Chesterton. The Scandal of dad 'The Hermit Clad in Crane Feathers' Brown 'The element of a Pin'. in R. van Gulik's The chinese language Maze Murders. turning out to be specialization and diversification have introduced a number of monographs and textbooks on more and more really good issues. notwithstanding, the "tree" of data of arithmetic and comparable fields doesn't develop in basic terms via placing forth new branches. It additionally occurs, as a rule actually, that branches which have been thouglit to be thoroughly disparate are without warning visible to be comparable. extra, the sort and point of class of arithmetic utilized in quite a few sci­ ences has replaced enormously lately: degree thought is used (non-trivially) in re­ gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding concept and the constitution of water meet each other in packing and overlaying conception; quantum fields, crystal defects and mathematical programming take advantage of homo­ topy thought; Lie algebras are correct to filtering; and prediction and electric engineering can use Stein spaces.

By Vladimir Rovenski

This monograph is predicated at the author's effects at the Riemannian ge­ ometry of foliations with nonnegative combined curvature and at the geometry of sub manifolds with turbines (rulings) in a Riemannian house of nonnegative curvature. the most thought is that such foliated (sub) manifolds might be decom­ posed while the size of the leaves (generators) is big. The equipment of research are as a rule artificial. The paintings is split into elements, which includes seven chapters and 3 appendices. Appendix A used to be written together with V. Toponogov. half 1 is dedicated to the Riemannian geometry of foliations. within the first few sections of bankruptcy I we provide a survey of the elemental effects on foliated gentle manifolds (Sections 1.1-1.3), and end in part 1.4 with a dialogue of the foremost challenge of this paintings: the function of Riemannian curvature within the research of foliations on manifolds and submanifolds.

By Lugo G.

By Klaus Ecker

* dedicated to the movement of surfaces for which the traditional speed at each element is given through the suggest curvature at that time; this geometric warmth move approach is termed suggest curvature circulate. * suggest curvature circulate and comparable geometric evolution equations are vital instruments in arithmetic and mathematical physics.  

By Jurgen Jost, Xianqing Li-Jost

By Owen Dearricott

Providing an up to date assessment of the geometry of manifolds with non-negative sectional curvature, this quantity offers a close account of the newest examine within the quarter. The lectures conceal a variety of subject matters resembling basic isometric team activities, circle activities on absolutely curved 4 manifolds, cohomogeneity one activities on Alexandrov areas, isometric torus activities on Riemannian manifolds of maximal symmetry rank, n-Sasakian manifolds, isoparametric hypersurfaces in spheres, touch CR and CR submanifolds, Riemannian submersions and the Hopf conjecture with symmetry. additionally integrated is an creation to the speculation of external differential systems.