Results 31 to 40 of about 587 (217)
On the local extension of Killing vector-fields in Ricci flat manifolds [PDF]
Journal of the American Mathematical Society, 2012 We revisit the extension problem for Killing vector-fields in smooth Ricci flat manifolds, and its relevance to the black hole rigidity problem. We prove both a stronger version of the main local extension result established earlier, as well as two types of results concerning non-extendibility. In particular, we show that one can find local, stationary,
Alexandru D. Ionescu, Sergiù Klainerman
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Energy and asymptotics of Ricci-flat 4-manifolds with a Killing field [PDF]
Proceedings of the American Mathematical Society, 2017 Given a complete, Ricci-flat 4-manifold with a Killing field, we give an estimate on the manifold's energy in terms of a certain asymptotic quantity of the Killing field. If the Killing field has no zeros and satisfies a certain asymptotic condition, the manifold is flat.
Brian Weber
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On the Perelman’s reduced entropy and Ricci flat manifolds with maximal volume growth [PDF]
Mathematische Annalen, 2012 9 ...
Liang Cheng, Anqiang Zhu
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Ricci-Flat Metrics on Vector Bundles Over Flag Manifolds [PDF]
Communications in Mathematical Physics, 2020 AbstractWe construct explicit complete Ricci-flat metrics on the total spaces of certain vector bundles over flag manifolds of the group SU(n), for all Kähler classes. These metrics are natural generalizations of the metrics of Candelas–de la Ossa on the conifold, Pando Zayas–Tseytlin on the canonical bundle over $$\mathbb {CP}^1\times \mathbb {CP}^1 ...
Dmitri Bykov +2 more
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Ricci almost solitons and gradient Ricci almost solitons in $(k,\mu)$-paracontact geometry
Boletim da Sociedade Paranaense de Matemática, 2019 The purpose of this paper is to study Ricci almost soliton and gradient Ricci almost soliton in $(k,\mu)$-paracontact metric manifolds. We prove the non-existence of Ricci almost soliton in a $(k,\mu)$-paracontact metric manifold $M$ with $k-1$ and whose
Uday Chand De, Krishanu Mandal
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Ricci-flat kahler manifolds and supersymmetry
Physics Letters B, 1980 Abstract A class of supersymmetric non-linear σ-models obtained previously is shown to generate a set of explicit Ricci-flat Kahler metrics of even complex dimension. The two-dimensional case is a self-dual gravitational instanton, very probably the Eguchi-Hansen metric, while higher dimensional cases may coincide with manifolds of Calabi.
Luis Alvarez-Gaumé, Daniel Z. Freedman
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L p $L^{p}$ harmonic 1-forms on conformally flat Riemannian manifolds
Journal of Inequalities and Applications, 2021 In this paper, we establish a finiteness theorem for L p $L^{p}$ harmonic 1-forms on a locally conformally flat Riemannian manifold under the assumptions on the Schrödinger operators involving the squared norm of the traceless Ricci form. This result can
Jing Li, Shuxiang Feng, Peibiao Zhao
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A gap theorem for Ricci-flat 4-manifolds
Differential Geometry and its Applications, 2015 Let $(M,g)$ be a compact Ricci-flat 4-manifold. For $p \in M$ let $K_{max}(p)$ (respectively $K_{min}(p)$) denote the maximum (respectively the minimum) of sectional curvatures at $p$. We prove that if $$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.
Bhattacharya, Atreyee, Seshadri, Harish
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Characteristics of Sasakian Manifolds Admitting Almost ∗-Ricci Solitons
Fractal and Fractional, 2023 This article presents some results of a geometric classification of Sasakian manifolds (SM) that admit an almost ∗-Ricci soliton (RS) structure (g,ω,X). First, we show that a complete SM equipped with an almost ∗-RS with ω≠ const is a unit sphere.
Vladimir Rovenski, Dhriti Sundar Patra
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η-Ricci Solitons on Sasakian 3-Manifolds
Annals of the West University of Timisoara: Mathematics and Computer Science, 2017 In this paper we study η-Ricci solitons on Sasakian 3-manifolds. Among others we prove that an η-Ricci soliton on a Sasakian 3-manifold is an η-Einstien manifold.
Majhi Pradip +2 more
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