The Experts below are selected from a list of 57882 Experts worldwide ranked by ideXlab platform
Sergei Tabachnikov - One of the best experts on this subject based on the ideXlab platform.
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pseudo riemannian geodesics and billiards
2009Co-Authors: Boris Khesin, Sergei TabachnikovAbstract:Abstract In Pseudo-Riemannian geometry the spaces of space-like and time-like geodesics on a Pseudo-Riemannian Manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. Furthermore, the space of all geodesics has a structure of a Jacobi Manifold. We describe the geometry of these structures and their generalizations. We also introduce and study pseudo-Euclidean billiards, emphasizing their distinction from Euclidean ones. We present a pseudo-Euclidean version of the Clairaut theorem on geodesics on surfaces of revolution. We prove pseudo-Euclidean analogs of the Jacobi–Chasles theorems and show the integrability of the billiard in the ellipsoid and the geodesic flow on the ellipsoid in a pseudo-Euclidean space.
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pseudo riemannian geodesics and billiards
2006Co-Authors: Boris Khesin, Sergei TabachnikovAbstract:Many classical facts in Riemannian geometry have their Pseudo-Riemannian analogs. For instance, the spaces of space-like and time-like geodesics on a Pseudo-Riemannian Manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. We discuss the geometry of these structures in detail, as well as introduce and study pseudo-Euclidean billiards. In particular, we prove pseudo-Euclidean analogs of the Jacobi-Chasles theorems and show the integrability of the billiard in the ellipsoid and the geodesic flow on the ellipsoid in a pseudo-Euclidean space.
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pseudo riemannian geodesics and billiards
2006Co-Authors: Boris Khesin, Sergei TabachnikovAbstract:Many classical facts in Riemannian geometry have their Pseudo-Riemannian analogs. For instance, the spaces of space-like and time-like geodesics on a Pseudo-Riemannian Manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. We discuss the geometry of these structures in detail, as well as introduce and study pseudo-Euclidean billiards. In particular, we prove pseudo-Euclidean analogs of the Jacobi-Chasles theorems and show the integrability of the billiard in the ellipsoid and the geodesic flow on the ellipsoid in a pseudo-Euclidean space.
Boris Khesin - One of the best experts on this subject based on the ideXlab platform.
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pseudo riemannian geodesics and billiards
2009Co-Authors: Boris Khesin, Sergei TabachnikovAbstract:Abstract In Pseudo-Riemannian geometry the spaces of space-like and time-like geodesics on a Pseudo-Riemannian Manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. Furthermore, the space of all geodesics has a structure of a Jacobi Manifold. We describe the geometry of these structures and their generalizations. We also introduce and study pseudo-Euclidean billiards, emphasizing their distinction from Euclidean ones. We present a pseudo-Euclidean version of the Clairaut theorem on geodesics on surfaces of revolution. We prove pseudo-Euclidean analogs of the Jacobi–Chasles theorems and show the integrability of the billiard in the ellipsoid and the geodesic flow on the ellipsoid in a pseudo-Euclidean space.
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pseudo riemannian geodesics and billiards
2006Co-Authors: Boris Khesin, Sergei TabachnikovAbstract:Many classical facts in Riemannian geometry have their Pseudo-Riemannian analogs. For instance, the spaces of space-like and time-like geodesics on a Pseudo-Riemannian Manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. We discuss the geometry of these structures in detail, as well as introduce and study pseudo-Euclidean billiards. In particular, we prove pseudo-Euclidean analogs of the Jacobi-Chasles theorems and show the integrability of the billiard in the ellipsoid and the geodesic flow on the ellipsoid in a pseudo-Euclidean space.
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pseudo riemannian geodesics and billiards
2006Co-Authors: Boris Khesin, Sergei TabachnikovAbstract:Many classical facts in Riemannian geometry have their Pseudo-Riemannian analogs. For instance, the spaces of space-like and time-like geodesics on a Pseudo-Riemannian Manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. We discuss the geometry of these structures in detail, as well as introduce and study pseudo-Euclidean billiards. In particular, we prove pseudo-Euclidean analogs of the Jacobi-Chasles theorems and show the integrability of the billiard in the ellipsoid and the geodesic flow on the ellipsoid in a pseudo-Euclidean space.
Dieter Lust - One of the best experts on this subject based on the ideXlab platform.
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flux formulation of dft on group Manifolds and generalized scherk schwarz compactifications
2016Co-Authors: Pascal Du Bosque, Falk Hassler, Dieter LustAbstract:A flux formulation of Double Field Theory on group Manifold is derived and applied to study generalized Scherk-Schwarz compactifications, which give rise to a bosonic subsector of half-maximal, electrically gauged supergravities. In contrast to the flux formulation of original DFT, the covariant fluxes split into a fluctuation and a background part. The latter is connected to a 2D-dimensional, pseudo Riemannian Manifold, which is isomorphic to a Lie group embedded into O(D,D). All fields and parameters of generalized diffeomorphisms are supported on this Manifold, whose metric is spanned by the background vielbein E A I ∈ GL(2D). This vielbein takes the role of the twist in conventional generalized Scherk-Schwarz compactifications. By doing so, it solves the long standing problem of constructing an appropriate twist for each solution of the embedding tensor. Using the geometric structure, absent in original DFT, E A I is identified with the left invariant Maurer-Cartan form on the group Manifold, in the same way as it is done in geometric Scherk-Schwarz reductions. We show in detail how the Maurer-Cartan form for semisimple and solvable Lie groups is constructed starting from the Lie algebra. For all compact embeddings in O(3, 3), we calculate E A I .
Wayne Rossman - One of the best experts on this subject based on the ideXlab platform.
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a loop group formulation for constant curvature subManifolds of pseudo euclidean space
2008Co-Authors: David Brander, Wayne RossmanAbstract:We give a loop group formulation for the problem of isometric immersions with flat normal bundle of a simply connected Pseudo-Riemannian Manifold $M_{c,r}^m$, of dimension $m$, constant sectional curvature $c \neq 0$, and signature $r$, into the pseudo-Euclidean space $\bf R_s^{m+k}$, of signature $s\geq r$. In fact these immersions are obtained canonically from the loop group maps corresponding to isometric immersions of the same Manifold into a Pseudo-Riemannian sphere or hyperbolic space $S_s^{m+k}$ or $H_s^{m+k}$, which have been known for some time. A simple formula is given for obtaining these immersions from those loop group maps.
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a loop group formulation for constant curvature subManifolds of pseudo euclidean space
2006Co-Authors: David Brander, Wayne RossmanAbstract:We give a loop group formulation for the problem of isometric immersions with flat normal bundle of a simply connected Pseudo-Riemannian Manifold $M_{c,r}^m$, of dimension $m$, constant sectional curvature $c \neq 0$, and signature $r$, into the pseudo-Euclidean space $\real_s^{m+k}$, of signature $s\geq r$. In fact these immersions are obtained canonically from the loop group maps corresponding to isometric immersions of the same Manifold into a Pseudo-Riemannian sphere or hyperbolic space $S_s^{m+k}$ or $H_s^{m+k}$, which have previously been studied. A simple formula is given for obtaining these immersions from those loop group maps.
Falk Hassler - One of the best experts on this subject based on the ideXlab platform.
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flux formulation of dft on group Manifolds and generalized scherk schwarz compactifications
2016Co-Authors: Pascal Du Bosque, Falk Hassler, Dieter LustAbstract:A flux formulation of Double Field Theory on group Manifold is derived and applied to study generalized Scherk-Schwarz compactifications, which give rise to a bosonic subsector of half-maximal, electrically gauged supergravities. In contrast to the flux formulation of original DFT, the covariant fluxes split into a fluctuation and a background part. The latter is connected to a 2D-dimensional, pseudo Riemannian Manifold, which is isomorphic to a Lie group embedded into O(D,D). All fields and parameters of generalized diffeomorphisms are supported on this Manifold, whose metric is spanned by the background vielbein E A I ∈ GL(2D). This vielbein takes the role of the twist in conventional generalized Scherk-Schwarz compactifications. By doing so, it solves the long standing problem of constructing an appropriate twist for each solution of the embedding tensor. Using the geometric structure, absent in original DFT, E A I is identified with the left invariant Maurer-Cartan form on the group Manifold, in the same way as it is done in geometric Scherk-Schwarz reductions. We show in detail how the Maurer-Cartan form for semisimple and solvable Lie groups is constructed starting from the Lie algebra. For all compact embeddings in O(3, 3), we calculate E A I .
