Some remarks on Hermitian manifolds satisfying Kähler-like conditions
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DOI: 10.1007/s00209-020-02598-2
Abstract: We study Hermitian metrics whose Bismut connection $\nabla^B$ satisfies the first Bianchi identity in relation to the SKT condition and the parallelism of the torsion of the Bimut connection. We obtain a characterization of complex… read more here.
Keywords: hermitian manifolds; condition; math; ahler like ... See more keywords
On Compact Hermitian Manifolds with Flat Gauduchon Connections
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DOI: 10.1007/s10114-018-7409-y
Abstract: Given a Hermitian manifold (Mn, g), the Gauduchon connections are the one parameter family of Hermitian connections joining the Chern connection and the Bismut connection. We will call $${\nabla ^s} = \left( {1 - \frac{s}{2}}… read more here.
Keywords: connection; flat gauduchon; gauduchon connections; compact hermitian ... See more keywords
Gradient estimate of positive eigenfunctions of sub-Laplacian on complete pseudo-Hermitian manifolds
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DOI: 10.1016/j.geomphys.2019.103577
Abstract: Abstract In this paper, we derive an explicit gradient estimate of positive solutions of Δ b u = − λ u on complete noncompact pseudo-Hermitian manifolds with bounded geometric conditions. As a consequence, we obtain… read more here.
Keywords: pseudo; pseudo hermitian; gradient estimate; hermitian manifolds ... See more keywords
The ∂-complex on weighted Bergman spaces on Hermitian manifolds
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DOI: 10.1016/j.jmaa.2020.123994
Abstract: Abstract In this paper, we investigate the ∂-complex on weighted Bergman spaces on Hermitian manifolds satisfying a certain holomorphicity/duality condition. This generalizes the situation of the Segal-Bargmann space in C n , studied earlier by… read more here.
Keywords: complex weighted; bergman spaces; spaces hermitian; weighted bergman ... See more keywords
Weak solutions of the Monge–Ampère equation on compact Hermitian manifolds
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DOI: 10.1142/s0129167x1740002x
Abstract: In this paper, we describe how pluripotential methods can be applied to study weak solutions of the complex Monge–Ampere equation on compact Hermitian manifolds. We indicate the differences between Kahler and non-Kahler setting. The results… read more here.
Keywords: solutions monge; weak solutions; compact hermitian; hermitian manifolds ... See more keywords
On the Gauduchon Curvature of Hermitian Manifolds
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DOI: 10.1142/s0129167x23500398
Abstract: It is shown that many results, previously believed to be properties of the Lichnerowicz Ricci curvature, hold for the Ricci curvature of all Gauduchon connections. We prove the existence of $t$--Gauduchon Ricci-flat metrics on the… read more here.
Keywords: curvature hermitian; curvature; gauduchon curvature; hermitian manifolds ... See more keywords