Results 21 to 30 of about 43,110 (140)

Generalized cylinders in semi-Riemannian and spin geometry [PDF]

, 2003
.We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to embeddings ...
Christian Bär, P. Gauduchon, Andrei Moroianu   +2 more
semanticscholar   +1 more source

Some Curvature Problems in Semi-Riemannian Geometry [PDF]

, 2010
In this survey article we review several results on the curvature of semi-Riemannian metrics which are motivated by the positive mass theorem. The main themes are estimates of the Riemann tensor of an asymptotically flat manifold and the construction of ...
AN Bernal, BL Reinhart, C Bär, D Maerten, E Witten, F Hirzebruch, F. Finster, F. Varela, FJ Tipler, G Huisken, H.L. Bray, HL Bray, P Yodzis, R Arnowitt, R Bartnik, R Schoen, R Schoen, RP Geroch, SK Donaldson, T Parker, WP Thurston   +20 more
core   +2 more sources

New Dimensions for Wound Strings: The Modular Transformation of Geometry to Topology [PDF]

, 2006
We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in hep-th/0510044. Milnor's theorem relates negative
A. Manning, B. Pioline, D. Knopf, David Starr, E. Witten, Eva Silverstein, J. Isenberg, J. Milnor, J. Polchinski, John McGreevy, N. A. Nekrasov, P. de la Harpe, Robert E. Gompf   +12 more
core   +5 more sources

Fill Radius and the Fundamental Group [PDF]

, 2009
In this note we relate the geometric notion of fill radius with the fundamental group of the manifold. We prove: ''Suppose that a closed Riemannian manifold M satisfies the property that its universal cover has bounded fill radius.
Ramachandran, Mohan, Wolfson, Jon
core   +2 more sources

Every conformal class contains a metric of bounded geometry [PDF]

, 2013
We show that on every manifold, every conformal class of semi-Riemannian metrics contains a metric $$g$$g such that each $$k$$kth-order covariant derivative of the Riemann tensor of $$g$$g has bounded absolute value $$a_k$$ak.
O. Müller, M. Nardmann
semanticscholar   +1 more source

Fourier and Gegenbauer expansions for a fundamental solution of the Laplacian in the hyperboloid model of hyperbolic geometry

, 2012
Due to the isotropy $d$-dimensional hyperbolic space, there exist a spherically symmetric fundamental solution for its corresponding Laplace-Beltrami operator.
Abramowitz M, Andrews G E, Beltrami E, Bers L, Byrd P F, Cohl H S, Cohl H S, Cohl H S, E G Kalnins, Erdélyi A, Erdélyi A, Fano U, Folland G B, Fox L, Gilbarg D, Gradshteyn I S, Grigor’yan A A, Grigor’yan A A, Grigor’yan A A, H S Cohl, Helgason S, Izmest’ev A A, Kalnins E G, Lee J M, Livio M, Losev A G, Magnus W, Morse P M, Olevskii˘ M N, Olver F W J, Olver F W J, Schoen R, Thurston W P, Trudeau R J, Vilenkin N Ja   +34 more
core   +2 more sources

On the total curvature and extrinsic area growth of surfaces with tamed second fundamental form [PDF]

, 2015
In this paper we show that a complete and non-compact surface immersed in the Euclidean space with quadratic extrinsic area growth has finite total curvature provided the surface has tamed second fundamental form and admits total curvature.
Brandao, Cristiane M., Gimeno, Vicent
core   +2 more sources

Initial State Privacy of Nonlinear Systems on Riemannian Manifolds

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT In this paper, we investigate initial state privacy protection for discrete‐time nonlinear closed systems. By capturing Riemannian geometric structures inherent in such privacy challenges, we refine the concept of differential privacy through the introduction of an initial state adjacency set based on Riemannian distances.
Le Liu, Yu Kawano, Antai Xie, Ming Cao
wiley   +1 more source

L^2-torsion of hyperbolic manifolds of finite volume

, 2008
Suppose $\bar{M}$ is a compact connected odd-dimensional manifold with boundary, whose interior $M$ comes with a complete hyperbolic metric of finite volume.
Lueck, Wolfgang, Schick, Thomas
core   +3 more sources

Holomorphic field theories and higher algebra

Bulletin of the London Mathematical Society, EarlyView.
Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons ...
Owen Gwilliam, Brian R. Williams
wiley   +1 more source