Integral Formulas in Riemannian Geometry PDF Download

Author: Kentarō Yano
Publisher: Marcel Dekker
ISBN:
Category : Mathematics
Languages : en
Pages : 176

View

Book Description

Author: Kentaro Yano
Publisher:
ISBN:
Category :
Languages : en
Pages : 156

View

Book Description

Author: Vladimir Rovenski
Publisher: Springer Nature
ISBN: 3030700674
Category : Mathematics
Languages : en
Pages : 319

View

Book Description
This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem of the Ricci curvature for the case of mixed curvature of foliations is examined. The book is divided into five chapters that deal with integral and variation formulas and curvature and dynamics of foliations. Different approaches and methods (local and global, regular and singular) in solving the problems are described using integral and variation formulas, extrinsic geometric flows, generalizations of the Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and 'computable' Finsler metrics. The book presents the state of the art in geometric and analytical theory of foliations as a continuation of the authors' life-long work in extrinsic geometry. It is designed for newcomers to the field as well as experienced geometers working in Riemannian geometry, foliation theory, differential topology, and a wide range of researchers in differential equations and their applications. It may also be a useful supplement to postgraduate level work and can inspire new interesting topics to explore.

Author: D H Howard Howard
Publisher: Oxford University Press, USA
ISBN: 9781470400866
Category : MATHEMATICS
Languages : en
Pages : 82

View

Book Description
This book shows that much of classical integral geometry can be derived from the coarea formula by some elementary techniques. Howard generalizes much of classical integral geometry from spaces of constant sectional curvature to arbitrary Riemannian homogeneous spaces. To do so, he provides a general definition of an integral invariant'' of a submanifold of the space that is sufficiently general enough to cover most cases that arise in integral geometry. Working in this generality makes it clear that the type of integral geometric formulas that hold in a space does not depend on the full group of isometries, but only on the isotropy subgroup. As a special case, integral geometric formulas that hold in Euclidean space also hold in all the simply connected spaces of constant curvature. Detailed proofs of the results and many examples are included. Requiring background of a one-term course in Riemannian geometry, this book may be used as a textbook in graduate courses on differential and integral geometry.

Author: Ralph Howard
Publisher: American Mathematical Soc.
ISBN: 0821825690
Category : Mathematics
Languages : en
Pages : 82

View

Book Description
This memoir investigates a method that generalizes the Chern-Federer kinematic formula to arbitrary homogeneous spaces with an invariant Riemannian metric, and leads to new formulas even in the case of submanifolds of Euclidean space.

Author: Detlef Laugwitz
Publisher: Academic Press
ISBN: 1483263983
Category : Mathematics
Languages : en
Pages : 251

View

Book Description
Differential and Riemannian Geometry focuses on the methodologies, calculations, applications, and approaches involved in differential and Riemannian geometry. The book first offers information on local differential geometry of space curves and surfaces and tensor calculus and Riemannian geometry. Discussions focus on tensor algebra and analysis, concept of a differentiable manifold, geometry of a space with affine connection, intrinsic geometry of surfaces, curvature of surfaces, and surfaces and curves on surfaces. The manuscript then examines further development and applications of Riemannian geometry and selections from differential geometry in the large, including curves and surfaces in the large, spaces of constant curvature and non-Euclidean geometry, Riemannian spaces and analytical dynamics, and metric differential geometry and characterizations of Riemannian geometry. The publication elaborates on prerequisite theorems of analysis, as well as the existence and uniqueness theorem for ordinary first-order differential equations and systems of equations and integrability theory for systems of first-order partial differential equations. The book is a valuable reference for researchers interested in differential and Riemannian geometry.

Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 0817646795
Category : Mathematics
Languages : en
Pages : 344

View

Book Description
This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.

Author: Liviu I Nicolaescu
Publisher: World Scientific
ISBN: 9811214832
Category : Mathematics
Languages : en
Pages : 701

View

Book Description
The goal of this book is to introduce the reader to some of the main techniques, ideas and concepts frequently used in modern geometry. It starts from scratch and it covers basic topics such as differential and integral calculus on manifolds, connections on vector bundles and their curvatures, basic Riemannian geometry, calculus of variations, DeRham cohomology, integral geometry (tube and Crofton formulas), characteristic classes, elliptic equations on manifolds and Dirac operators. The new edition contains a new chapter on spectral geometry presenting recent results which appear here for the first time in printed form.

Author: Victor Palamodov
Publisher: Birkhäuser
ISBN: 3034879415
Category : Mathematics
Languages : en
Pages : 171

View

Book Description
This book covers facts and methods for the reconstruction of a function in a real affine or projective space from data of integrals, particularly over lines, planes, and spheres. Recent results stress explicit analytic methods. Coverage includes the relations between algebraic integral geometry and partial differential equations. The first half of the book includes the ray, the spherical mean transforms in the plane or in 3-space, and inversion from incomplete data.

Author: Chaohao Gu
Publisher: Springer
ISBN: 3540478833
Category : Mathematics
Languages : en
Pages : 259

View

Book Description
The DD6 Symposium was, like its predecessors DD1 to DD5 both a research symposium and a summer seminar and concentrated on differential geometry. This volume contains a selection of the invited papers and some additional contributions. They cover recent advances and principal trends in current research in differential geometry.