Results 11 to 20 of about 44,281 (143)

Riemannian Geometry and the Fundamental Theorem of Algebra [PDF]

, 2011
If a (non-constant) polynomial has no zero, then a certain Riemannian metric is constructed on the two dimensional sphere. Several geometric arguments are then shown to contradict this fact.
J. M. Almira, Alfonso Romero
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The Reciprocal of the Fundamental Theorem of Riemannian Geometry [PDF]

, 2009
The fundamental theorem of Riemannian geometry is inverted for analytic Christoffel symbols. The inversion formula, henceforth dubbed Ricardo's formula, is obtained without ancillary assumptions. Even though Ricardo's formula can mathematically give the full answer, it is argued that the solution should be taken only up to a constant conformal factor ...
Héctor H. Calderón
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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
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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
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Geometry without topology as a new conception of geometry [PDF]

, 2001
A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T-geometric one are considered. T-geometry is built only on the basis of information included in the metric (distance between two points).
Rylov, Yuri A.
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On Almost Paracontact Almost Paracomplex Riemannian Manifolds [PDF]

, 2018
Almost paracontact manifolds of an odd dimension having an almost paracomplex structure on the paracontact distribution are studied. The components of the fundamental (0,3)-tensor, derived by the covariant derivative of the structure endomorphism and the
Manev, Mancho, Tavkova, Veselina
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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
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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
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Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group [PDF]

, 2016
We use a Riemannnian approximation scheme to define a notion of intrinsic Gaussian curvature for a Euclidean C2 -smooth surface in the Heisenberg group H away from characteristic points, and a notion of intrinsic signed geodesic curvature for Euclidean ...
Balogh, Zoltan M., Tyson, Jeremy T., Vecchi, Eugenio   +2 more
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The noncommutative Lorentzian cylinder as an isospectral deformation

, 2003
We present a new example of a finite-dimensional noncommutative manifold, namely the noncommutative cylinder. It is obtained by isospectral deformation of the canonical triple associated to the Euclidean cylinder. We discuss Connes' character formula for
Brodzki, Connes, Connes, Connes, Connes, Connes, Dubois-Violette, Elliot, Estrada, Gracia-Bondı́a, Green, Kamani, Konechny, Landsman, Langmann, Nest, Parfionov, Ramazan, Rennie, Rieffel, Rieffel, Rieffel, Rieffel, Schweitzer, Seiberg, Strohmaier, Várilly, Várilly, W. D. van Suijlekom   +28 more
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