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Existence of Generalized Maxwell–Einstein Metrics on Completions of Certain Line Bundles
MathematicsIn Kähler geometry, Calabi extremal metrics serves as a class of more available special metrics than Kähler metrics with constant scalar curvatures, as a generalization of Kähler Einstein metrics. In recent years, Maxwell–Einstein metrics (or conformally
Jing Chen, Daniel Guan
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New Einstein metrics on the Lie group $SO(n)$ which are not naturally reductive [PDF]
, 2015 We obtain new invariant Einstein metrics on the compact Lie groups $SO(n)$ ($n \geq 7$) which are not naturally reductive. This is achieved by imposing certain symmetry assumptions in the set of all left-invariant metrics on $SO(n)$ and by computing ...
A. Arvanitoyeorgos +2 more
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Invariant Einstein metrics on generalized Wallach spaces [PDF]
, 2015 Invariant Einstein metrics on generalized Wallach spaces have been classified except SO(k + l + m)/SO(k) × SO(l) × SO(m). In this paper, we first give a survey on the study of invariant Einstein metrics on generalized Wallach spaces, and prove that there
Zhiqi Chen, Yu. G. Nikonorov
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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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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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On the Curvature of Conic Kähler–Einstein Metrics [PDF]
The Journal of Geometric Analysis, 2017 We prove a regularity result for Monge-Ampère equations degenerate along smooth divisor on Kaehler manifolds in Donaldson's spaces of $β$-weighted functions. We apply this result to study the curvature of Kaehler metrics with conical singularities along divisors and give a geometric sufficient condition on the divisor for its boundedness.
Arezzo, C +2 more
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Hidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain Scaling Limits
Symmetry, Integrability and Geometry: Methods and Applications, 2012 The hidden symmetries of higher dimensional Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein-Sasaki ones.
Mihai Visinescu, Eduard Vîlcu
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G2-metrics arising from non-integrable special Lagrangian fibrations
Complex Manifolds, 2019 We study special Lagrangian fibrations of SU(3)-manifolds, not necessarily torsion-free. In the case where the fiber is a unimodular Lie group G, we decompose such SU(3)-structures into triples of solder 1-forms, connection 1-forms and equivariant 3 × 3 ...
Chihara Ryohei
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Smooth and singular Kahler-Einstein metrics [PDF]
, 2014 Smooth Kähler–Einstein metrics have been studied for the past 80 years. More recently, singular Kähler–Einstein metrics have emerged as objects of intrinsic interest, both in differential and algebraic geometry, as well as a powerful tool in better ...
Yanir A. Rubinstein
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The nonexistence of quasi-Einstein metrics [PDF]
Pacific Journal of Mathematics, 2010 We study complete Riemannian manifolds satisfying the equation $Ric+\nabla^2 f-\frac{1}{m}df\otimes df=0$ by studying the associated PDE $Δ_f f + mμe^{2f/m}=0$ for $μ\leq 0$. By developing a gradient estimate for $f$, we show there are no nonconstant solutions.
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