Results 81 to 90 of about 13,435 (197)
Mathematika, Volume 70, Issue 2, April 2024.Abstract Determinantal point processes exhibit an inherent repulsive behavior, thus providing examples of very evenly distributed point sets on manifolds. In this paper, we study the so‐called harmonic ensemble, defined in terms of Laplace eigenfunctions on the sphere Sd$\mathbb {S}^d$ and the flat torus Td$\mathbb {T}^d$, and the so‐called spherical ...
Bence Borda +2 more
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Shadow Images of a Rotating Dyonic Black Hole with a Global Monopole Surrounded by Perfect Fluid
Universe, 2020 In this paper, we revisit the rotating global monopole metric and extend the metric to a rotating dyonic global monopole in the presence of a perfect fluid. We then show that the surface topology at the event horizon, related to the metric computed, is a
Sumarna Haroon +2 more
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Unification of Gravity and Internal Interactions
Fortschritte der Physik, Volume 72, Issue 1, January 2024.Abstract In the gauge theoretic approach of gravity, general relativity is described by gauging the symmetry of the tangent manifold in four dimensions. Usually the dimension of the tangent space is considered to be equal to the dimension of the curved manifold. However, the tangent group of a manifold of dimension d is not necessarily SOd$SO_d$.
Spyros Konitopoulos +2 more
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Heat Kernel Embeddings, Differential Geometry and Graph Structure
Axioms, 2015 In this paper, we investigate the heat kernel embedding as a route to graph representation. The heat kernel of the graph encapsulates information concerning the distribution of path lengths and, hence, node affinities on the graph; and is found by ...
Hewayda ElGhawalby, Edwin R. Hancock
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A small cusped hyperbolic 4‐manifold
Bulletin of the London Mathematical Society, Volume 56, Issue 1, Page 176-187, January 2024.Abstract By gluing some copies of a polytope of Kerckhoff and Storm's, we build the smallest known orientable hyperbolic 4‐manifold that is not commensurable with the ideal 24‐cell or the ideal rectified simplex. It is cusped and arithmetic, and has twice the minimal volume.
Stefano Riolo
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The Effects of Finite Distance on the Gravitational Deflection Angle of Light
Universe, 2019 In order to clarify the effects of the finite distance from a lens object to a light source and a receiver, the gravitational deflection of light has been recently reexamined by using the Gauss−Bonnet (GB) theorem in differential geometry (Ishihara
Toshiaki Ono, Hideki Asada
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Discrete curvature and the Gauss-Bonnet theorem
, 2010 For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss--Bonnet theorem is shown to follow.
Arnlind, Joakim +2 more
core
A new mass for asymptotically flat manifolds
, 2013 In this paper we introduce a mass for asymptotically flat manifolds by using the Gauss-Bonnet curvature. We first prove that the mass is well-defined and is a geometric invariant, if the Gauss-Bonnet curvature is integrable and the decay order $\tau ...
Ge, Yuxin, Wang, Guofang, Wu, Jie
core
A topological Gauss-Bonnet theorem
Journal of Differential Geometry, 1978 The generalized Gauss-Bonnet theorem of Allendoerfer- Weil [1] and Chern [2] has played an important role in the development of the relationship between modern differential geometry and algebraic topology, providing in particular one of the primary stimuli for the theory of characteristi c classes.
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Gauss-Bonnet theorems for noncompact surfaces [PDF]
Proceedings of the American Mathematical Society, 1982 For The( rem A, see also [1]. Such an M is homeomorphic to a compact surface with p points deleted. A neighborhood of each point is homeomorphic to S' X R+, and by forming the gradient flow associated to a Morse function on M [5], the metric on the cusp S1 X R+ can be chosen to be of the form g11(O, t)d02 + g22(O, t)dt2. Reparametrizing R+ by arclength
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