Results 11 to 20 of about 581 (202)
The collapsing geometry of almost Ricci-flat 4-manifolds [PDF]
Commentarii Mathematici Helvetici, 2020 We consider Riemannian 4-manifolds that Gromov–Hausdorff converge to a lower dimensional limit space, with the Ricci tensor going to zero. Among other things, we show that if the limit space is two dimensional then under some mild assumptions, the limiting four dimensional geometry away from the curvature blowup region is semiflat Kähler.
John Lott
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Methods of holonomy theory for Ricci-flat Riemannian manifolds [PDF]
Journal of Mathematical Physics, 1991 Compact, Ricci-flat Riemannian manifolds often arise in physical applications, either as a technical device or as models of ‘‘internal’’ space. The idea of extending the holonomy group of such a manifold to a larger gauge group (‘‘embedding the connection in the gauge group’’) plays a fundamental role in the ‘‘manifold compactification’’ approach to ...
Brett McInnes
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Approximate Ricci-flat Metrics for Calabi-Yau Manifolds [PDF]
We outline a method to determine analytic Kähler potentials with associated approximately Ricci-flat Kähler metrics on Calabi-Yau manifolds. Key ingredients are numerically calculating Ricci-flat Kähler potentials via machine learning techniques and fitting the numerical results to Donaldson's Ansatz. We apply this method to the Dwork family of quintic
Lee, Seung-Joo, Lukas, Andre
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A gap theorem for Ricci-flat 4-manifolds [PDF]
Differential Geometry and its Applications, 2012 Let $(M,g)$ be a compact Ricci-flat 4-manifold. For $p \in M$ let $K_{max}(p)$ (respectively $K_{min}(p)$) denote the maximum (respectively the minimum) of sectional curvatures at $p$. We prove that if $$K_{max} (p) \le \ -c K_{min}(p)$$ for all $p \in M$, for some constant $c$ with $0 \leq c < \frac{2+\sqrt 6}{4}$, then $(M,g)$ is flat.
Atreyee Bhattacharya, Harish Seshadri
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The Global Geometry of Ricci-Flat Manifolds
Ricci-flat manifolds are fundamental in differential geometry and theoretical physics, particularly General Relativity and string theory. Characterized by a vanishing Ricci curvature tensor, these manifolds embody a profound geometric equilibrium, mirroring the absence of matter or energy in Einstein's vacuum field equations. This paper offers a novel,
SÉRGIO DE ANDRADE, PAULO
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Static Ricci-flat 5-manifolds admitting the 2-sphere [PDF]
Classical and Quantum Gravity, 2006 We examine, in a purely geometrical way, static Ricci-flat 5-manifolds admitting the 2-sphere and an additional hypersurface-orthogonal Killing vector. These are widely studied in the literature, from different physical approaches, and known variously as the Kramer - Gross - Perry - Davidson - Owen solutions.
Kayll Lake
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Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold [PDF]
Mathematica Bohemica, 2022 The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection.
Payel Karmakar
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∗-Ricci Tensor on α-Cosymplectic Manifolds
Advances in Mathematical Physics, 2022 In this paper, we study α-cosymplectic manifold M admitting ∗-Ricci tensor. First, it is shown that a ∗-Ricci semisymmetric manifold M is ∗-Ricci flat and a ϕ-conformally flat manifold M is an η-Einstein manifold. Furthermore, the ∗-Weyl curvature tensor
M. R. Amruthalakshmi +3 more
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∗-Ricci tensor on (κ,μ)-contact manifolds
AIMS Mathematics, 2022 We introduce the notion of semi-symmetric ∗-Ricci tensor and illustrate that a non-Sasakian (κ,μ)-contact manifold is ∗-Ricci semi-symmetric or has parallel ∗-Ricci operator if and only if it is ∗-Ricci flat. Then we find that among the non-Sasakian (κ,μ)
Rongsheng Ma, Donghe Pei
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DEGENERATIONS OF RICCI-FLAT CALABI–YAU MANIFOLDS [PDF]
Communications in Contemporary Mathematics, 2013 This paper is a sequel to [Continuity of extremal transitions and flops for Calabi–Yau manifolds, J. Differential Geom.89 (2011) 233–270]. We further investigate the Gromov–Hausdorff convergence of Ricci-flat Kähler metrics under degenerations of Calabi–Yau manifolds. We extend Theorem 1.1 in [Continuity of extremal transitions and flops for Calabi–Yau
Rong, Xiaochun, Zhang, Yuguang
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