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Kähler–Einstein metrics and eigenvalue gaps
Communications in Analysis and Geometry, 2023 The existence of Kahler-Einstein metrics on a Fano manifold is characterized in terms of a uniform gap between 0 and the first positive eigenvalue of the Cauchy-Riemann operator on smooth vector fields. It is also characterized by a similar gap between 0 and the first positive eigenvalue for Hamiltonian vector fields.
Guo, Bin, Phong, Duong H., Sturm, Jacob
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Journal of High Energy Physics, 2021 The ultrashort unitary (4, 0) supermultiplet of 6d superconformal algebra OSp(8∗|8) reduces to the CPT-self conjugate supermultiplet of 4d superconformal algebra SU(2, 2|8) that represents the fields of maximal N = 8 supergravity. The graviton in the (4,
Murat Günaydin
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Five-dimensional vacuum Einstein spacetimes in C-metric like coordinates
, 2010 A 5-dimensional Einstein spacetime with (non)vanishing cosmological constant is analyzed in detail. The metric is in close analogy with the 4-dimensional massless uncharged C-metric in many aspects.
BIN ZHU +4 more
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Asymptotics of ACH-Einstein Metrics [PDF]
The Journal of Geometric Analysis, 2013 We study the boundary asymptotics of ACH metrics which are formally Einstein. In terms of the partially integrable almost CR structure induced on the boundary at infinity, existence and uniqueness of such formal asymptotic expansions are studied. It is shown that there always exist formal solutions to the Einstein equation if we allow logarithmic terms,
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Kropina Metrics with Isotropic Scalar Curvature via Navigation Data
MathematicsThrough an interesting physical perspective and a certain contraction of the Ricci curvature tensor in Finsler geometry, Akbar-Zadeh introduced the concept of scalar curvature for the Finsler metric.
Yongling Ma +2 more
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Uniqueness of optimal symplectic connections
Forum of Mathematics, Sigma, 2021 Consider a holomorphic submersion between compact Kähler manifolds, such that each fibre admits a constantscalar curvature Kähler metric. When the fibres admit continuous automorphisms, a choice of fibrewise constant scalarcurvature Kähler metric is not ...
Ruadhaí Dervan, Lars Martin Sektnan
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Ricci flow on K\"ahler-Einstein manifolds
, 2003 In our previous paper math.DG/0010008, we develop some new techniques in attacking the convergence problems for the K\"ahler Ricci flow. The one of main ideas is to find a set of new functionals on curvature tensors such that the Ricci flow is the ...
Chen, X. X., Tian, G.
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Rigidity of quasi-Einstein metrics
Differential Geometry and its Applications, 2011 We call a metric quasi-Einstein if the $m$-Bakry-Emery Ricci tensor is a constant multiple of the metric tensor. This is a generalization of Einstein metrics, which contains gradient Ricci solitons and is also closely related to the construction of the warped product Einstein metrics.
Case, Jeffrey, Shu, Yu-Jen, Wei, Guofang
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D-Homothetically Deformed Kenmotsu Metric as a Ricci Soliton
Annales Mathematicae Silesianae, 2019 In this paper we study the nature of Ricci solitons in D-homo-thetically deformed Kenmotsu manifolds. We prove that η -Einstein Kenmotsu metric as a Ricci soliton remains η -Einstein under D-homothetic deformation and the scalar curvature remains ...
Kumar D.L. Kiran, Nagaraja H.G., Venu K.
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A note on the relationship between solutions of Einstein, Ramanujan and Chazy equations
, 2011 The Einstein equation for the Friedmann-Robertson-Walker metric plays a fundamental role in cosmology. The direct search of the exact solutions of the Einstein equation even in this simple metric case is sometime a hard job.
Esmakhanova, Kuralay +3 more
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