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Locally Conformal Kähler and Hermitian Yang-Mills Metrics
The author shows that if a locally conformal Kähler metric is Hermitian Yang-Mills with respect to itself with Einstein constant c ≤ 0, then it is a...
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Scalar curvatures in almost Hermitian geometry and some applications
On an almost Hermitian manifold, there are two Hermitian scalar curvatures associated with a canonical Hermitian connection. In this paper, two...
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Vanishing Theorems on Holomorphic Lie Algebroids
The paper describes a Bochner-type study for holomorphic horizontal vector fields defined on a holomorphic Finsler algebroid E . We obtain in this...
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Hopf cyclic cohomology and Hodge theory for proper actions on complex manifolds
We introduce two Hopf algebroids associated to a proper and holomorphic Lie group action on a complex manifold. We prove that the cyclic cohomology...
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Hessian Comparison and Spectrum Lower Bound of Almost Hermitian Manifolds
The authors obtain a complex Hessian comparison for almost Hermitian manifolds, which generalizes the Laplacian comparison for almost Hermitian...
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Kenmotsu statistical manifolds and warped product
A notion of a Kenmotsu statistical manifold is introduced, which is locally obtained as the warped product of a holomorphic statistical manifold and...
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Isotropic Lagrangian submanifolds in the homogeneous nearly Kähler S3 × S3
We show that isotropic Lagrangian submanifolds in a 6-dimensional strict nearly Kähler manifold are totally geodesic. Moreover, under some weaker...
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Interpolation of geometric structures compatible with a pseudo Riemannian metric
Let ( M , g ) be a pseudo Riemannian manifold. We consider four geometric structures on M compatible with g : two almost complex and two almost product...
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Nearly Kähler Submanifolds of a Space Form
In this article, we study isometric immersions of nearly Kähler manifolds into a space form (especially Euclidean space) and show that every nearly...
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On blow-ups and resolutions of Hermitian-symplectic and strongly Gauduchon metrics
In this note, we study the blow-ups of Hermitian-symplectic manifolds and strongly Gauduchon manifolds along a point or compact complex submanifold....
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Nonpositively curved almost Hermitian metrics on product of compact almost complex manifolds
In this paper, we give a classification of almost Hermitian metrics with nonpositive holomorphic bisectional curvature on a product of compact almost...
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Locally Conformally Kähler Structures on Homogeneous Spaces
We will discuss in this paper homogeneous locally conformally Kähler (or shortly homogeneous l.c.K.) manifolds and locally homogeneous l.c.K....
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Almost Kähler Ricci Flows and Einstein and Lagrange–Finsler Structures on Lie Algebroids
In this work we investigate Ricci flows of almost Kähler structures on Lie algebroids when the fundamental geometric objects are completely...
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Novikov homology, jump loci and Massey products
Let X be a finite CW complex, and ρ : π 1 ( X ) → GL( l , ℂ) a representation. Any cohomology class α ∈ H 1 ( X , ℂ) gives rise to a deformation γ ...
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Almost Contact Lagrangian Submanifolds of Nearly Kaehler 6-Sphere
For a Lagrangian submanifold M of S 6 with nearly Kaehler structure, we provide conditions for a canonically induced almost contact metric structure...