In this paper we give classification of Kähler surfaces of generalized Calabi type.
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48 results for “generalized Calabi type”
The paper describes a specific type of Kähler surfaces.
problem Understanding QCH Kähler surfaces with quasi-constant holomorphic sectional curvature.
method Detailed description of generalized Calabi type QCH Kähler surfaces.
result Detailed description of QCH Kähler surfaces of generalized Calabi type.
We study type one generalized complex and generalized Calabi--Yau manifolds. We introduce a cohomology class that obstructs the existence of a globally defined, closed 2-form which agrees with the symplectic form on the leaves of the generalized complex structure, the twisting class. We prove that in a compact, type on…
The paper proves properties of Kähler surfaces with zero scalar curvature.
problem Characterizing Kähler surfaces with zero scalar curvature.
method Analyzing families of generalized Taub-Nut Kähler surfaces and Burn's metric.
result Proves that certain Kähler surfaces are QCH and of specific types.
The paper proves Calabi-Bernstein type results for minimal and maximal surfaces in 3D and 3D-L spacetime.
problem Characterizing minimal and maximal surfaces in 3D and 3D-L spacetime.
method Analyzing surfaces with specific properties and using geometric and functional methods.
result Calabi-Bernstein type results for critical points of a weighted area functional in and .
New Calabi-Yau metrics converge polynomially to Calabi model space.
problem Finding complete Calabi-Yau metrics with polynomial convergence rate.
method Defined new metrics on Calabi-Yau complements with ample normal bundles.
result Uniqueness of these metrics within a cohomology class.
Solves Calabi-Yau equation on complex manifolds with non-positive astheno-Ricci curvature.
problem Solving the form type Calabi-Yau equation on complex manifolds.
method Defined astheno-Ricci curvature and proved existence of solution under non-positive curvature condition.
result Existence of solution for Calabi-Yau equation with non-positive astheno-Ricci curvature.
We discuss mirror symmetry in generalized Calabi-Yau compactifications of type II string theories with background NS fluxes. Starting from type IIB compactified on Calabi-Yau threefolds with NS three-form flux we show that the mirror type IIA theory arises from a purely geometrical compactification on a different class…
Researchers extend period maps for Calabi-Yau types using modified Kato-Nakayama-Usui construction.
problem Existence of weak fans for non-classical period maps of weight 3 Calabi-Yau type.
method Modified Kato-Nakayama-Usui construction for period maps of weight 3 Calabi-Yau type.
result Existence of weak fans for a large class of period maps of weight 3 Calabi-Yau type.
New complete hypersurfaces found in affine geometry.
problem Finding new complete hypersurfaces in affine geometry.
method Classifying special Calabi hypersurfaces and solving equations.
result Found a class of new Euclidean and Calabi complete affine hypersurfaces.
Stability of Type IIA flow ensures Kähler properties of Calabi-Yau 3-folds.
problem Ensuring the Kähler property of Calabi-Yau 3-folds under symplectic deformations.
method Established dynamical stability of Type IIA flow near stationary points.
result Stability of Type IIA flow ensures the stability of Kähler properties under symplectic deformations.
Complete Calabi-Yau metrics on C^{N+1} are constructed.
problem Constructing complete Calabi-Yau metrics on C^{N+1} for N >= 3.
method Generalized Gibbons-Hawking ansatz with gluing procedure to overcome volume-form defects.
result Calabi-Yau metrics with tangent cone R^N are constructed.
Uniform estimates for Calabi-Yau degenerations proved.
problem Calabi-Yau degenerations of polarised algebraic manifolds.
method Uniform Skoda and -estimates for Kähler potentials.
result Uniform Skoda type estimate and -estimate for Calabi-Yau Kähler potentials proved.
In this paper we study several issues related to the generation of superpotential induced by background Ramond-Ramond fluxes in compactification of Type IIA string theory on Calabi-Yau four-folds. Identifying BPS solitons with D-branes wrapped over calibrated submanifolds in a Calabi-Yau space, we propose a general for…
Study on asymptotic behavior of Taub-NUT type solitons and construction of new ALF Calabi-Yau metrics.
problem Asymptotic behavior of steady gradient Kähler-Ricci solitons of Taub-NUT type.
method Determination of asymptotic cone, special case analysis, and construction of new metrics using Tian-Yau-Hein method.
result Construction of new ALF Calabi-Yau metrics on quotients of the Taub-NUT type soliton.
The paper constructs invariant Calabi-Yau structures on complexified symmetric spaces.
problem Constructing invariant Calabi-Yau structures on complexified symmetric spaces.
method Solutions of a Monge-Ampère type equation.
result Existence of solutions to the Monge-Ampère type equation.
Solves generalized Kähler Calabi-Yau problem on compact manifolds.
problem Calabi conjecture in generalized Kähler geometry.
method New local deformation result, Bismut Ricci curvature transgression formula, generalized Kähler-Ricci flow.
result Global existence and convergence of flow for initial data in generalized Kähler class of Kähler Calabi-Yau structure.
In this paper we construct explicit smooth solutions to the Strominger system on generalized Calabi-Gray manifolds, which are compact non-Kähler Calabi-Yau 3-folds with infinitely many distinct topological types and sets of Hodge numbers.
Form-type Calabi-Yau equations on Kähler manifolds of nonnegative orthogonal bisectional curvaturemath.DG
In this paper we prove the existence and uniqueness of the form-type Calabi-Yau equation on Kähler manifolds of nonnegative orthogonal bisectional curvature.
Solves Calabi-Yau equation on symplectic manifolds using measurable Kahler metrics.
problem Solving the Calabi-Yau equation on symplectic manifolds.
method Global deformation of almost complex structures compatible with symplectic form, constructing measurable Lipschitz Kahler metric.
result Existence theorem for solutions to the one-form type Calabi-Yau equation on closed symplectic manifolds.
We study Riemannian geometry of canonical Kahler-Einstein currents on projective Calabi-Yau varieties and canonical models of general type with crepant singularities. We prove that the metric completion of the regular part of such a canonical current is a compact metric length space homeomorphic to the original project…
It is known that there exist Calabi-Yau structures on the complexifications of symmetric spaces of compact type. In this paper, we describe the Calabi-Yau structures of the complexified symmetric spaces in terms of the Schwarz's theorem in detail. We consider the case where the Calabi-Yau structure arises from the Riem…
The study constructs balanced and rigid curves on specific types of hypersurfaces and complete intersections.
problem Constructing balanced and rigid curves on Calabi-Yau and general-type complete intersections.
method Balanced and rigid curves are constructed using specific hypersurfaces and complete intersections.
result Rigid curves of various genera and balanced rational curves of high degrees are constructed.
New Spin(7) manifolds created from Calabi-Yau bundles.
problem Creating complete non-compact Spin(7) manifolds.
method Building on -bundles over AC Calabi-Yau manifolds.
result First known examples of complete toric Spin(7) manifolds.
Polyhomogeneous expansions for Calabi-Yau metrics near singularities.
problem Analyzing metrics near conical singularities of Calabi-Yau conifolds.
method Weighted Melrose-type blow-ups, gluing, and solving complex Monge-Ampère equations.
result Polyhomogeneous expansions of smooth Calabi-Yau metrics on resolutions and smoothings.
Estimates symplectic Calabi-Yau equation using Cheng-Yau method.
problem Estimating solutions to the Calabi-Yau equation on symplectic 4-manifolds.
method Applies a Cheng-Yau type estimate in the symplectic setting.
result Proves an a priori estimate for the symplectic Calabi-Yau equation.
The Ricci Calabi functional is a functional on the space of Kähler metrics of Fano manifolds. Its critical points are called generalized Kähler Einstein metrics. In this article, we show that the Hessian of the Ricci Calabi functional is non-negative at generalized Kähler Einstein metrics. As its application, we give a…
Study deformations of Calabi-Yau foliations using Kuranishi spaces.
problem Deforming Calabi-Yau foliations and understanding their properties.
method Analysis of three types of deformations (unfoldings, holomorphic, transversally holomorphic) using Kuranishi spaces.
result Smoothness of and product structure of .
Study on flows of G2-structures on contact Calabi-Yau 7-manifolds.
problem Analyzing the behavior of G2-structures under Laplacian and Hitchin flows.
method Investigation of Laplacian and Hitchin flows on contact Calabi-Yau 7-manifolds.
result Ancient solutions of the Laplacian flow with finite time Type I singularity and immortal solutions of the Laplacian coflow with infinite time Type IIb singularity.
Study solves equations on tori for Calabi-Yau problems.
problem Solving equations on tori for Calabi-Yau problems.
method Study of fully nonlinear equations on flat tori.
result Solvability of equations on tori established.
Study on non-Kähler Calabi-Yau manifolds and their geometric structures.
problem Holomorphic geometric structures on non-Kähler compact complex manifolds.
method Beauville-Bogomolov decomposition and weak Bochner principle.
result Rigidity of Vaisman Calabi-Yau manifolds implies they are Kodaira manifolds.
For a one parameter family of Calabi-Yau threefolds, Green, Griffiths and Kerr have expressed the total singularities in terms of the degrees of Hodge bundles and Euler number of the general fiber. In this paper, we show that the total singularities can be expressed by the sum of asymptotic values of BCOV invariants, s…
The paper proves estimates for vortex-type equations on compact Riemann surfaces.
problem Estimating vortex-type equations on compact Riemann surfaces.
method Proves \emph{a priori} estimates for vortex-type equations.
result Recover existing estimates for vortex bundle Monge-Ampère equation, prove existence and uniqueness for Calabi-Yang-Mills equations, and get estimates for vortex equation.
The paper describes a new type of Kähler surfaces and their properties.
problem Characterizing and understanding Kähler surfaces of generalized orthotoric type.
method Introducing a distinguished orthonormal frame and integrating structure equations.
result A new way to classify and understand Kähler surfaces, especially orthotoric ones.
We construct a family of Calabi-Yau metrics on $\C^3$ with properties analogous to the Taub-NUT metric on $\C^2$, and construct a family of Calabi-Yau 3-fold metric models on the positive and negative vertices of SYZ fibrations with properties analogous to the Ooguri-Vafa metric.
On a complete Calabi-Yau manifold with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon-Hein. We prove this result by proving a Liouville type theorem for harmonic -forms, which follows from a new local …
Study explores unstable 3-forms on Calabi-Yau 3-folds.
problem Understanding degenerations of Calabi-Yau 3-folds via 3-forms.
method Investigates geometries of 3-forms on symplectic 6-manifolds.
result Unstable 3-forms reveal rich geometric properties related to SYZ conjecture.
We study the intrinsic geometry of hypersurfaces in Calabi-Yau manifolds of real dimension 6 and, more generally, SU(2)-structures on 5-manifolds defined by a generalized Killing spinor. We prove that in the real analytic case, such a 5-manifold can be isometrically embedded as a hypersurface in a Calabi-Yau manifold i…
Combinatorial p-th Calabi Flows for Total Geodesic Curvatures in hyperbolic background geometrymath.DG
The paper finds circle packings with specific curvatures in hyperbolic geometry.
problem Finding circle packings with prescribed total geodesic curvatures and discrete Gaussian curvatures.
method Established existence and rigidity via variational principle, introduced combinatorial p-th Calabi flows.
result Introduced combinatorial p-th Calabi flows to find circle packings with prescribed curvatures.
We construct a geometric model of eight-dimensional manifolds and realize them in the context of type II string theory. These eight-manifolds are constructed by non-trivial fibrations over Calabi-Yau two-folds. These give rise to eight-dimensional non-Kahler Hermitian manifolds with structure. The eight…
New Kähler metrics generalize Calabi's and relate to Fano manifolds.
problem Existence of extremal Kähler metrics on Fano manifolds.
method Introducing -extremal Kähler metrics and relating them to multiplier Hermitian-Einstein metrics.
result Existence of -extremal Kähler metrics implies existence of multiplier Hermitian-Einstein metrics on Fano manifolds.
Machine learning predicts Hodge numbers of Calabi-Yau four-folds.
problem Predicting Hodge numbers of Calabi-Yau manifolds using machine learning.
method Supervised learning of Hodge numbers h^1,1 and h^3,1 for complete intersection Calabi-Yau four-folds.
result A two-branch network with feature enhancement achieves 98% precision for predicting h^3,1.
The curvature properties of a specific type of 6-manifold are explored.
problem Curvature identities on almost Calabi-Yau 6-manifolds with torsion.
method Analysis of the Nijenhuis tensor, torsion connection, and Ricci solitons.
result The curvature of the torsion connection is symmetric and vanishes if the norm of the torsion or scalar curvature is constant.
We develop some techniques to study the adiabatic limiting behaviour of Calabi-Yau metrics on the total space of a fibration, and obtain strong control near the singular fibres by imposing restrictions on the singularity types. We prove a uniform lower bound on the metric up to the singular fibre, under fairly general …
We introduce the coupled Ricci-Calabi functional and the coupled H-functional which measure how far from a coupled Kähler-Einstein metric in the sense of Hultgren-Witt Nyström. We first give corresponding moment weight type inequalities which estimate each functional in terms of algebraic invariants. Secondly, we give …
In this paper, we prove the extensions of Bonnet--Myers' type theorems obtained by Calabi and Cheeger--Gromov--Taylor via Bakry--Emery Ricci curvature, which generalize the results of \cite{FG, Lim1, Wan, Wang, WW, Wu}.
Superminimal surfaces in certain Einstein manifolds have a Calabi-Yau property.
problem Characterizing superminimal surfaces in specific Einstein manifolds.
method Utilizing twistor spaces and properties of holomorphic Legendrian curves.
result Superminimal surfaces in self-dual or anti-self-dual Einstein four-manifolds can be uniformly approximated by complete superminimal surfaces.
In this paper we obtain generalized Calabi-type compactness criteria for complete Riemannian manifolds that allow the presence of negative amounts of Ricci curvature. These, in turn, can be rephrased as new conditions for the positivity, for the existence of a first zero and for the nonoscillatory-oscillatory behaviour…