Nearly Kähler and Kähler-Codazzi type manifolds are defined in a very similar way. We prove that nearly Kähler type manifolds have sense just in Hermitian and para-Hermitian contexts, and that Kähler-Codazzi type manifolds reduce to Kähler type manifolds in all the four Hermitian, para-Hermitian, Norden and product Rie…
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48 results for “Kahler manifolds”
Eigenvalue problem for Kähler metrics on compact manifolds.
problem Eigenvalue problem for the Laplacian on Kähler manifolds.
method Introducing -extremal Kähler metrics and deducing conditions for extremality.
result Conditions for a Kähler metric to be -extremal.
New non-Kähler examples of generalized Kähler manifolds constructed via mapping tori.
problem Constructing new non-Kähler generalized Kähler manifolds.
method Starting from a 3-torus and a compact Kähler manifold, constructing via mapping tori.
result Obtained new non-Kähler examples and recovered known examples of generalized Kähler solvmanifolds.
The study finds conditions for almost-Kähler 4-manifolds to be Kähler.
problem Conditions for almost-Kähler 4-manifolds to be Kähler.
method Analyzes harmonic self-dual Weyl curvature and constant scalar curvature.
result Compact almost-Kähler 4-manifolds with harmonic self-dual Weyl curvature and constant scalar curvature are Kähler if .
Study on Kähler manifolds sharing submanifolds, proving projective implies relative.
problem Understanding Kähler manifolds sharing submanifolds.
method Proving properties of weak and strict relatives Kähler manifolds.
result If one Kähler manifold is projective and shares a submanifold with another, they are relatives.
Proof of flow convergence on Fano manifolds.
problem Convergence of Kahler-Ricci flow on Fano manifolds.
method Recent techniques in geometry and analysis.
result Convergence of Kahler-Ricci flow on Fano manifolds.
A note on first eigenvalue estimates by coupling methods in Kähler and quaternion Kähler manifoldsmath.PR
Study eigenvalue estimates on Kähler and quaternion Kähler manifolds.
problem Estimating first eigenvalues in Kähler and quaternion Kähler manifolds.
method Using Kendall-Cranston coupling to analyze eigenvalues.
result Eigenvalue estimates in terms of dimension, diameter, and curvature.
Study Brownian motions and heat kernel bounds on Kähler and quaternion Kähler manifolds.
problem Understanding Brownian motions and heat kernel bounds on specific geometric manifolds.
method Sharp Laplacian comparison theorems and Cheeger-Yau type lower bounds for heat kernels.
result Sharp Cheeger-Yau type lower bounds for heat kernels and Dirichlet eigenvalues of metric balls.
Extends Hodge theory to nearly Kähler manifolds of arbitrary dimensions.
problem Generalize Hodge-theoretic results to nearly Kähler manifolds of arbitrary dimensions.
method Apply Hodge theory to nearly Kähler manifolds of arbitrary dimensions, relating Hodge numbers to Betti numbers.
result Hodge numbers of compact nearly Kähler manifolds are related to Betti numbers in the same way as on a compact Kähler manifold.
Diameter theorems on Kähler and quaternionic Kähler manifolds under a positive lower curvature boundmath.DG
Study diameter bounds on Kähler and quaternionic Kähler manifolds with positive curvature.
problem Determine diameter bounds for Kähler and quaternionic Kähler manifolds under curvature positivity.
method Define orthogonal Bakry-Émery tensor, study diameter theorems, and derive Bonnet-Myers type bounds.
result Sharper diameter bounds than in Riemannian case under specific curvature assumptions.
The paper studies rigidity results for harmonic forms on Kähler manifolds.
problem Understanding harmonic forms on Kähler manifolds.
method Analyzes rigidity results for harmonic -forms in complete Kähler manifolds.
result Shows several rigidity results and applications to non-compact Kähler manifolds.
Study deformations of compact Kähler hyperbolic manifolds.
problem Investigate the deformation openness of Kähler hyperbolicity.
method Propose modified versions of Kähler hyperbolicity as a tool.
result Provide a first step towards understanding deformations.
The paper extends Gray's result to quaternion-Kähler manifolds.
problem Understanding quaternion-Kähler manifolds with non-negative quaternionic sectional curvature.
method Introducing quaternionic sectional curvature, proving Wolf spaces have non-negative curvature, and using nearly Kähler twistor spaces.
result Every quaternion-Kähler manifold with non-negative quaternionic sectional curvature is a Wolf space.
On astheno-Kähler manifoldsmath.DG
Survey of astheno-Kähler manifolds and their challenges.
problem Understanding astheno-Kähler manifolds and their existence.
method Review of classical findings and recent developments.
result Challenges in the existence of astheno-Kähler manifolds.
We extend Calabi ansatz over Kähler-Einstein manifolds to Sasaki-Einstein manifolds. As an application we prove the existence of a complete scalar-flat Kähler metric on Kähler cone manifolds over Sasaki-Einstein manifolds. In particular there exists a complete scalar-flat Kähler metric on the toric Kähler cone manifold…
Kähler-Ricci flow on Kähler manifolds converges to negative Kodaira dimension
problem Convergence of scalar curvature in Kähler-Ricci flow
method Uniform -entropy or uniform Sobolev inequality
result Scalar curvature converges to negative Kodaira dimension
We derive an interpolation version of constrained matrix Li-Yau-Hamilton estimate on Kähler manifolds. As a result, we first get a constrained matrix Li-Yau-Hamilton estimate for heat equation on a Kähler manifold with fixed Kähler metric. Secondly, we get a corresponding estimate for forward conjugate heat equation on…
In this paper we obtain a stability theorem of generalized Kahler structures with one pure spinor under small deformations of generalized complex structures. (This is analogous to the stability theorem of Kahler manifolds by Kodaira-Spencer.) We apply the stability theorem to a class of compact Kahler manifolds which a…
Formulae for curvature of quaternionic Kähler manifolds derived from hyper-Kähler data.
problem Deriving curvature formulae for quaternionic Kähler manifolds.
method Using HK/QK correspondence and Levi-Civita connection, we express curvature in terms of hyper-Kähler data.
result Formulae for curvature of quaternionic Kähler manifolds, including norm of curvature tensor.
We prove six-dimensional nearly Kähler manifolds are Einstein.
problem Characterizing six-dimensional nearly Kähler manifolds.
method Combining known results and partial differential equations.
result Nearly Kähler six-manifolds are Einstein.
The study explores geometric properties of hyperbolic cohomology classes on Kähler manifolds.
problem Understanding the geometric effects of hyperbolic cohomology classes on Kähler manifolds.
method Introducing Kähler topologically hyperbolic manifolds and proving spectral gap theorems for positive holomorphic Hermitian vector bundles.
result Kähler topologically hyperbolic manifolds are not uniruled nor bimeromorphic to compact Kähler manifolds with trivial first real Chern class.
The study explores weakly -Kähler hyperbolic manifolds.
problem Generalization and application of weakly -Kähler hyperbolic manifolds.
method Investigation of generalizations and applications.
result Exploration of weakly -Kähler hyperbolic manifolds.
New vanishing theorems for harmonic and pluriharmonic functions on Kähler and quaternionic Kähler manifolds.
problem Vanishing theorems for harmonic and pluriharmonic functions on Kähler and quaternionic Kähler manifolds.
method Utilized refined Kato type inequalities and Böchner technique to generalize results to -integrable pluriharmonic functions and harmonic 1-forms.
result Proved vanishing property of pluriharmonic functions with finite energy on complete Kähler manifolds.
Kähler manifold loop space inherits Kähler structure and is complete.
problem Characterizing the geometric properties of loop spaces of Kähler manifolds.
method Proving the Kähler structure and completeness of the loop space.
result The loop space of a Kähler manifold is complete and inherits a Kähler structure.
H-minimal Lagrangian submanifolds in general Kähler manifolds generalize special Lagrangian submanifolds in Calabi-Yau manifolds. In this paper we will use the deformation theory of H-minimal Lagrangian submanifolds in Kähler manifolds to construct minimal Lagrangian torus in certain Kähler-Einstein manifolds with nega…
We derive some elliptic differential inequalities from the Weitzenböck formulas for the traceless Ricci tensor of a Kähler manifold with constant scalar curvature and the Bochner tensor of a Kähler-Einstein manifold respectively. Using elliptic estimates and maximum principle, some and pinching result…
The paper proves rigidity properties of holomorphic isometries into homogeneous Kähler manifolds.
problem Rigidity of holomorphic isometries into homogeneous Kähler manifolds.
method Analyzing Kähler-Ricci solitons, flat spaces, and homogeneous bounded domains.
result Strong extensions of rigidity results in previous studies.
A locally conformally Kähler (LCK) manifold is a complex manifold covered by a Kähler manifold, with the covering group acting by homotheties. We show that if such a compact manifold X admits a holomorphic submersion with positive dimensional fibers at least one of which is of Kähler type, then X is globally conformall…
Kähler cones over Sasakian manifolds are flat if projectively induced.
problem Characterizing Kähler cones over Sasakian manifolds.
method Relating Kähler potentials and using Ricci-flatness.
result Kähler cones over regular Sasakian manifolds are flat if projectively induced.
A locally conformally Kahler (LCK) manifold is a manifold which is covered by a Kahler manifold, with the deck transform group acting by homotheties. We show that the blow-up of a compact LCK manifold along a complex submanifold admits an LCK structure if and only if this submanifold is globally conformally Kahler. We …
We prove that every projective special Kähler manifold with \emph{regular boundary behaviour} is complete and defines a family of complete quaternionic Kähler manifolds depending on a parameter . We also show that, irrespective of its boundary behaviour, every complete projective special Kähler manifold with \e…
The paper generalizes inequalities on almost Kähler manifolds.
problem Generalizing inequalities on almost Kähler manifolds.
method Considered Donaldson gauge functional and twisted Aubin functionals.
result Generalized inequality between Aubin functionals.
Study eigenvalues of p-Laplacian on quaternionic Kähler manifolds.
problem Finding lower bounds for eigenvalues of p-Laplacian on quaternionic Kähler manifolds.
method Analytical proofs for both Neumann and Dirichlet boundary conditions.
result Established lower bounds for eigenvalues on compact quaternionic Kähler manifolds.
Computes Weyl group of Kähler toric manifold isometries.
problem Computing the Weyl group of Kähler toric manifold isometries.
method Analyzes the group of holomorphic isometries of a Kähler toric manifold with real analytic Kähler metric.
result Computed the Weyl group of the group of holomorphic isometries.
We show that Lagrangian submanifolds in six-dimensional nearly Kähler (non Kähler) manifolds and in twistor spaces $Z\sp{4n+2}$ over quaternionic Kähler manifolds $Q\sp{4n}$ are minimal. Moreover, we will prove that any Lagrangian submanifold in a nearly Kähler manifold splits into a product of two Lagrangian s…
The paper explores symmetries in Kähler manifolds using Ricci tensor properties.
problem Investigating symmetries in Kähler manifolds involving Ricci tensor.
method Analyzing properties of Kähler-Einstein spaces and their generalizations.
result Clarified the geometric role of holomorphic Ricci pseudosymmetry and established new criteria for Kähler manifolds to be Einstein.
Study symplectically aspherical Kähler manifolds with unique properties.
problem Existence and properties of symplectically aspherical Kähler manifolds.
method Detailed study and analysis of geometric and topological features.
result Existence of symplectically aspherical Kähler manifolds with large fundamental groups.
The paper explores curvature positivity on Kähler and quasi-Kähler flag manifolds.
problem Analyzing curvature positivity on specific geometric structures.
method Investigation of Griffiths and dual-Nakano positivity for curvature of Chern connections on Kähler and quasi-Kähler flag manifolds.
result Classification of Kähler flag manifolds with Griffiths semi-positive curvature and restrictions for quasi-Kähler flag manifolds.
A product of Kähler manifolds also carries a Kähler metric. In this short note we would like to study the product of generalized Kähler manifolds, compact or not. The results we get extend the known results (balanced, SKT, sG manifolds), and are optimal in the compact case. Hence we can give new non-trivial example…
The Hodge theorem connects cohomology groups on compact Kähler manifolds.
problem Establishing a relationship between cohomology groups on compact Kähler manifolds.
method Proving the Hodge decomposition theorem on compact d-Kähler manifolds.
result Hodge decomposition theorem on compact d-Kähler manifolds.
The paper proves conditions for compact complex manifolds to be Kahler outside analytic subsets.
problem Conditions for compact complex manifolds to be Kahler outside an analytic subset.
method Analyzes balanced manifolds and uses Hironaka's examples to prove theorems.
result Compact complex manifolds that are Kahler outside an analytic subset are balanced.
Study on Kähler Finsler manifolds with curvature bounds, proving theorems.
problem Understanding Kähler Finsler manifolds with curvature constraints.
method Analyzing partial parallelism of complex structure, proving theorems.
result Generalized comparison theorem for positively curved Kähler Finsler manifolds.
New submersions found in nearly Kähler geometry.
problem Exploring submersions in nearly Kähler geometry.
method Using reducible holonomy representations and connections with parallel skew torsion.
result Parallel 3--Sasaki manifolds admit 1-dimensional submersions onto nearly Kähler orbifolds.
Paper studies Kähler-Ricci flow convergence on Fano manifolds.
problem Uniform convergence of Kähler-Ricci flow on Fano manifolds.
method Analyzes flow behavior with varied initial metrics and complex structures.
result Proves uniqueness of Kähler-Ricci solitons in diffeomorphism orbits.
Nearly Kähler manifolds are the Riemannian 6-manifolds admitting real Killing spinors. Equivalently, the Riemannian cone over a nearly Kähler manifold has holonomy contained in G2. In this paper we study the deformation theory of nearly Kähler manifolds, showing that it is obstructed in general. More precisely, we show…
The paper explores -Kähler structures on complex manifolds and their properties.
problem Addressing conjectures on specific types of complex manifolds and their structures.
method Analyzing -Kähler nilmanifolds and holomorphically parallelizable nilmanifolds, deriving necessary conditions for smooth curves of -Kähler structures, studying cohomology classes, and providing examples.
result Derives necessary conditions for the existence of smooth curves of -Kähler structures and provides examples of compact complex manifolds with -Kähler structures.
Survey on Kähler-Ricci flow solutions.
problem Existence of solutions for Kähler-Ricci flow.
method Survey of recent developments.
result Discussion of solutions existing for all positive times.
Compact Kähler manifolds with positive curvature have contractible covers.
problem Compact Kähler manifolds with positive sectional curvature.
method Proves contractibility of universal cover.
result The universal covering of a compact Kähler manifold with small positive sectional curvature is contractible.