Last edited by Takinos
Wednesday, July 22, 2020 | History

2 edition of Pseudo-riemannian geometry, [delta]-invariants and applications found in the catalog.

# Pseudo-riemannian geometry, [delta]-invariants and applications

## by Bang-Yen Chen

Written in English

Subjects:
• Riemannian Geometry,
• Riemannian manifolds,
• Submanifolds,
• Invariants

• Edition Notes

Includes bibliographical references (p. 439-462) and indexes.

Classifications The Physical Object Statement Bang-Yen Chen LC Classifications QA649 .C4825 2011 Pagination xxxii, 477 p. : Number of Pages 477 Open Library OL25232322M ISBN 10 9814329630 ISBN 10 9789814329637 LC Control Number 2011377751 OCLC/WorldCa 728077572

When the signature has a single negative the geometry is often called Lorentzian instead of pseudo-Riemannian. This geometry still inherits the concepts of the manifold, the metric, and points, of which the point remains an undefined primitive. However, Lorentzian geometry (due to its usual application in physics) frequently renamed these concepts. In differential geometry, the Einstein tensor is used to express the curvature of a pseudo-Riemannian manifold. In general relativity, it occurs in the Einstein field equations for gravitation that describe spacetime curvature in a manner consistent with .

In this work, we show that the thermodynamic phase space is naturally endowed with a non-integrable connection, defined by all of those processes that annihilate the Gibbs one-form, i.e., reversible processes. We argue that such a connection is invariant under re-scalings of the connection one-form, whilst, as a consequence of the non-integrability of the connection, its Cited by: Get this from a library! Ricci flow and the Poincaré conjecture. [John Morgan; Gang Tian] -- "This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is.

The book is also wonderful for its breadth. It is not a "tensor calculus" book, or a "differential geometry" book. It is really best described as a "geometrical methods" book "with applications to theoretical physics." Yet unlike most examples of this now-cliched subject, the breadth of material is matched by a cohesion of style/5. Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

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### Pseudo-riemannian geometry, [delta]-invariants and applications by Bang-Yen Chen Download PDF EPUB FB2

Semi-Riemannian geometry: with applications to relativity Barrett O'Neill This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry) - the study of a smooth manifold furnished with a metric tensor of arbitrary signature.

This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry.

Nevertheless, these books do not focus on (pseudo)-Riemannian geometry per se, but on general differential geometry, trying to introduce as many concepts as possible for the needs of modern theoretical physics.

Most purely mathematical books on Riemannian geometry do not treat the pseudo-Riemannian case (although many results are exactly the same). In differential geometry, a geodesic (/ ˌ dʒ iː ə ˈ d ɛ s ɪ k, ˌ dʒ iː Pseudo-riemannian geometry d iː-,-z ɪ k /) is a curve representing in some sense the shortest path between two points in a surface, or more generally in a Riemannian is a generalization of the notion of a "straight line" to a more general terms "geodesic" and "geodetic" come from geodesy, the science of.

In Section 5, we define the pseudo Riemannian Hausdorff dimension and prove Theorem Finally, the last section is devoted to the proof of Theorem 2 Pseudo-Riemannian Hyperbolic Geometry. In this section we introduce the pseudo-Riemannian hyperbolic space |${\mathbb{H}}^{p,q}$| and go over its basic properties.

Recently I started to read Amari's "Information Geometry and Its Pseudo-riemannian geometry. I quickly stumbled upon some (apparent) inconsistencies. I'm looking for a book that talks about Riemannian Geometry on Manifolds with boundary.

Unfortunately, I only found some results in articles, no systematic treatises. Newest riemannian-geometry. [21] B.-Y. Chen, Pseudo-Riemannian Geometry, delta-inv ariants and Applications; W ord Scientiﬁc Pub- lishing, Hackensac k, NJ, [22] B. Author: Bang-Yen Chen. The tetrad formalism is an approach to general relativity that generalizes the choice of basis for the tangent bundle from a coordinate basis to the less restrictive choice of a local basis, i.e.

a locally defined set of four linearly independent vector fields called a tetrad. In the tetrad formalism, all tensors are represented in terms of a chosen basis. In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection.

The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed with a metric, allowing distances to be measured on that differential geometry, an affine connection can be defined without reference to a metric, and many.

Intelligent Control and Automation pseudo-Riemannian geometry framework, the three quadratic forms, functions applied to the bipartite-Red and tripartite. Introduction and history. Historically, at the turn of the 20th century, the covariant derivative was introduced by Gregorio Ricci-Curbastro and Tullio Levi-Civita in the theory of Riemannian and pseudo-Riemannian geometry.

[1] Ricci and Levi-Civita (following ideas of Elwin Bruno Christoffel) observed that the Christoffel symbols used to define the curvature could also.

@article{osti_, title = {The principal bundle of biframes associated with space-time and its applications in general relativity and gauge theories}, author = {Hammon, K.S.}, abstractNote = {In this dissertation the author introduces a new principal fiber bundle, the bundle of biframes, over spacetime.

It is shown that the biframe bundle is a natural geometrical arena in which to. ∗Contribution to the Proceedings of the ESI semester “Geometry of Pseudo-Riemannian Man-ifolds with Applications in Physics” (Vienna, ) organized by D. Alekseevsky, H. Baum and J. Konderak. To appear in the volume ‘Recent developments in pseudo-Riemannian geometry’Cited by:   Abstract.

We introduce the flow of metrics on a foliated Riemannian manifold (M g), whose velocity along the orthogonal (to the foliation $$\mathcal{F}$$) distribution $$\mathcal{D}$$ is proportional to the mixed scalar curvature, Scal flow preserves harmonicity of foliations and is used to examine the question: When does a foliation admit a metric with a given Cited by: 4.

pseudo-Riemannian manifold. In brief, time and space together comprise a curved four-dimensional non-Euclidean geometry. Consequently, the practitioner of GR must be familiar with the fundamental geometrical properties of curved spacetime. In particu-lar, the laws of physics must be expressed in a form that is valid independently of anyFile Size: KB.

For more background on principal ∞-connections see also at ∞-Chern-Weil theory introduction. History. Around D’Auria and Fré noticed, in GeSuGra, that the intricacies of various supergravity classical field theories have a strikingly powerful reformulation in terms of super semifree differential graded-commutative algebras.

They defined various such super dg. Physics for Scientists and Engineers: Foundations and Connections - Ebook written by Debora M. Katz. Read this book using Google Play Books app on your PC, android, iOS devices.

Download for offline reading, highlight, bookmark or take notes while you read Physics for Scientists and Engineers: Foundations and Connections. Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron"measurement") is a branch of mathematicsconcerned with questions of shape, size, relative position of figures, and the properties of space.

A mathematician who works in the field of geometry is called a ry arose independently in a number of early cultures as a body of practical. The Christoffel symbols provide a concrete representation of the connection of (pseudo-)Riemannian geometry in terms of coordinates on the manifold.

Additional concepts, such as parallel transport, geodesics, etc. can then be expressed in terms of Christoffel symbols. ISBN: OCLC Number: Description: 1 online resource: Contents: Frontmatter --Contents --Introduction --Part I: Dissipative geometry and general relativity theory Pseudo-Riemannian geometry and general relativity Dynamics of universe models Anisotropic and homogeneous universe models.

Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space. The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration.• The book “Artiﬁcial Black Holes”, edited by Novello, Visser, and Volovik [].

-dimensional Lorentzian (pseudo–Riemannian) geometry. The metric depends algebraically on the density, velocity of ﬂow, and local speed of sound in the delta-function contribution at the vortex core) implies, via Stokes’ theorem, that.

In many posts on this blog, such as Geometry on Curved Spaces and Connection and Curvature in Riemannian Geometry, we have discussed the subject of differential geometry, usually in the context of have discussed what is probably its most famous application to date, as the mathematical framework of general relativity, which in turn is the foundation of .