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Download Differential Geometry of Lightlike Submanifolds by Krishan L. Duggal, Bayram Sahin PDF

By Krishan L. Duggal, Bayram Sahin

This is often the 1st systematic account of the most ends up in the speculation of lightlike submanifolds of semi-Riemannian manifolds that have a geometrical constitution, equivalent to nearly Hermitian, nearly touch metric or quaternion K?hler. utilizing those buildings, the booklet offers attention-grabbing sessions of submanifolds whose geometry is particularly wealthy. The publication additionally comprises hypersurfaces of semi-Riemannian manifolds, their use commonly relativity and Osserman geometry, half-lightlike submanifolds of semi-Riemannian manifolds, lightlike submersions, display conformal submersions, and their purposes in harmonic maps. easy buildings and definitions are provided as initial history in each bankruptcy. The presentation explores functions and indicates a number of open questions. This self-contained monograph presents updated learn in lightlike geometry and is meant for graduate scholars and researchers simply getting into this box.

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Download A Treatise on the Differential Geometry of Curves and by Luther Pfahler Eisenhart PDF

By Luther Pfahler Eisenhart

Created particularly for graduate scholars by way of a number one author on arithmetic, this advent to the geometry of curves and surfaces concentrates on difficulties that scholars will locate such a lot worthwhile.

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Download Cartan for Beginners: Differential Geometry Via Moving by Thomas A. Ivey, J. M. Landsberg PDF

By Thomas A. Ivey, J. M. Landsberg

This booklet is an advent to Cartan's method of differential geometry. critical tools in Cartan's geometry are the idea of external differential structures and the strategy of relocating frames. This publication provides thorough and sleek remedies of either topics, together with their functions to either vintage and modern problems.

It starts off with the classical geometry of surfaces and easy Riemannian geometry within the language of relocating frames, besides an user-friendly creation to external differential platforms. Key innovations are built incrementally with motivating examples resulting in definitions, theorems, and proofs.

Once the fundamentals of the equipment are verified, the authors advance functions and complex subject matters. One remarkable program is to advanced algebraic geometry, the place they extend and replace vital effects from projective differential geometry.
The ebook gains an creation to $G$-structures and a therapy of the speculation of connections. The Cartan equipment can be utilized to procure specific recommendations of PDEs through Darboux's technique, the strategy of features, and Cartan's approach to equivalence.

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Download Heat Kernels for Elliptic and Sub-elliptic Operators: by Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato PDF

By Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

This monograph is a unified presentation of a number of theories of discovering particular formulation for warmth kernels for either elliptic and sub-elliptic operators. those kernels are vital within the conception of parabolic operators simply because they describe the distribution of warmth on a given manifold in addition to evolution phenomena and diffusion methods.

The paintings is split into 4 major components: half I treats the warmth kernel through conventional equipment, corresponding to the Fourier rework approach, paths integrals, variational calculus, and eigenvalue growth; half II bargains with the warmth kernel on nilpotent Lie teams and nilmanifolds; half III examines Laguerre calculus functions; half IV makes use of the tactic of pseudo-differential operators to explain warmth kernels.

issues and features:

•comprehensive therapy from the viewpoint of certain branches of arithmetic, resembling stochastic methods, differential geometry, unique capabilities, quantum mechanics, and PDEs;

•novelty of the paintings is within the various equipment used to compute warmth kernels for elliptic and sub-elliptic operators;

•most of the warmth kernels computable via straight forward features are coated within the work;

•self-contained fabric on stochastic methods and variational equipment is included.

Heat Kernels for Elliptic and Sub-elliptic Operators is a perfect reference for graduate scholars, researchers in natural and utilized arithmetic, and theoretical physicists drawn to figuring out alternative ways of forthcoming evolution operators.

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Download The Geometry of Supermanifolds by C. Bartocci, U. Bruzzo, Daniel Hernández-Ruipérez PDF

By C. Bartocci, U. Bruzzo, Daniel Hernández-Ruipérez

'Et moi, ... si favait III mmment en revenir, One carrier arithmetic has rendered the je n'y serais aspect aile: ' human race. It has positioned CXlUImon feel again Iules Verne the place it belongs. at the topmost shelf subsequent to the dUlty canister lahelled 'discarded non- The sequence i. divergent; for this reason we are able to do anything with it. Eric T. Bell O. Hesvi.ide arithmetic is a device for notion. A hugely helpful software in an international the place either suggestions and non linearities abound. equally, every kind of elements of arithmetic function instruments for different components and for different sciences. employing an easy rewriting rule to the quote at the correct above one reveals such statements as: 'One carrier topology has rendered mathematical physics .. .'; 'One carrier common sense has rendered com puter technology .. .'; 'One carrier class thought has rendered arithmetic .. .'. All arguably precise. And all statements available this manner shape a part of the raison d't!tre of this sequence.

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Download Exterior Differential Systems and Equivalence Problems by Kichoon Yang PDF

By Kichoon Yang

This monograph offers a concise but basic account of external differential method concept in order that it may be fast utilized to difficulties. the 1st a part of the monograph, Chapters 1-5, bargains with the final thought: the Cartan-Kaehler theorem is proved, the notions of involution and prolongation are rigorously laid out, quasi-linear differential platforms are tested intimately, and specific examples of the Spencer cohomology teams and the attribute sort are given. the second one a part of the monograph, Chapters 6 and seven, offers with functions to difficulties in differential geometry: the isometric embedding theorem of Cartan-Janet and its quite a few geometric ramifications are mentioned, an explanation of the Andreotti-Hill theorem at the O-R embedding challenge is given, and embeddings of summary projective constructions are mentioned.
For researchers and graduate scholars who would favor an outstanding creation to external differential platforms. This quantity can also be relatively worthwhile to these whose paintings contains differential geometry and partial differential equations.

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