Smooth deformation of Moishezon manifolds preserves their Moishezon property.
problem Preserving Moishezon property under smooth deformation.
method Smooth deformation over a unit disk in C.
result Deformation limit of Moishezon manifolds is Moishezon.
A mathematical model describes deforming manifolds with precise vectors and fields.
problem Modeling and describing the deformation of complex manifolds in practical applications.
method Proposes a modified differential dynamic model with constraints on spatial and temporal continuity, presenting deforming vector and field.
result Demonstrates the effectiveness of an autonomous deforming field in data dimension reduction tasks.
The paper studies deformations of cohesive modules on complex manifolds.
problem Deformation theory of cohesive modules on compact complex manifolds.
method Development of Kuranishi maps and obstructions for deformations of cohesive modules.
result Generalization of deformation theory for holomorphic vector bundles and coherent sheaves.
The paper studies curvature changes on manifolds with boundary.
problem Investigating conformal deformations of curvature on manifolds with boundary.
method Establishing sufficient conditions for positive scalar curvature and mean convex boundary, exploring further deformation scenarios.
result Conditions for conformal deformations to complete metrics with positive scalar curvature and mean convex boundary.
Study on deformation theory of nearly G2 manifolds with obstructions.
problem Deformation theory of nearly G2 manifolds with obstructions.
method Study of real Killing spinors and cohomology of nearly G2 manifolds.
result Infinitesimal deformations of nearly G2 structures are obstructed in general.
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.
We consider some natural infinitesimal Einstein deformations on Sasakian and 3-Sasakian manifolds. Some of these are infinitesimal deformations of Killing spinors and further some integrate to actual Killing spinor deformations. In particular, on 3-Sasakian 7 manifolds these yield infinitesimal Einstein deformations pr…
Computes spectral Einstein functional for Witten deformation on even-dimensional spin manifolds.
problem Calculating the spectral Einstein functional for a specific deformation.
method Computes the spectral Einstein functional for the Witten deformation on even-dimensional spin manifolds.
result Computed the spectral Einstein functional for the Witten deformation on even-dimensional spin manifolds.
Study calculates deformations of instantons on a specific Spin(7)-manifold.
problem Analyzing instantons on a specific Spin(7)-manifold. method Deformation theory developed by the author.
result Virtual dimensions of moduli spaces of instantons calculated.
Study on solitons in deformed Kenmotsu manifolds with specific vector fields.
problem Analyzing geometric solitons in deformed Kenmotsu manifolds.
method Examined almost Riemann and Ricci solitons in a D-homothetically deformed Kenmotsu manifold with specific vector fields. result Explicitly obtained Ricci and scalar curvatures for some cases, provided a lower bound for Ricci curvature.
Study infinitesimal deformations of Killing spinors on nearly parallel G2-manifolds.
problem Infinitesimal deformations of Killing spinors on nearly parallel G2-manifolds.
method Examined using the correspondence between nearly parallel G2-structures and Killing spinors.
result Identified that the space of Rarita-Schwinger fields coincides with a subspace of the eigenspace of the Laplacian.
Study on deformations of holomorphic Cartan geometries, focusing on flat cases.
problem Deformation of holomorphic Cartan geometries on complex manifolds.
method Computing infinitesimal deformations and analyzing the forgetful map.
result The forgetful map from infinitesimal deformations of a flat holomorphic Cartan geometry to the underlying flat principal bundle is an isomorphism.
Constructs deformations of Vaisman manifolds preserving foliations.
problem Deforming Vaisman manifolds while maintaining their canonical foliations.
method Uses a basic 1-form with specific properties to construct transverse deformations.
result Basic 1-forms exist in abundance for constructing deformations.
New integrable deformations for topological hierarchies from Frobenius manifolds.
problem Integrable deformations of topological hierarchies from Frobenius manifolds.
method Construction of integrable deformations with polynomial tau-structures.
result Conjecture of universal object for Riemann--Hopf hierarchy.
In this thesis, we study deformations of compact holomorphic Poisson manifolds and algebraic Poisson schemes in the framework of Kodaira-Spencer's analytic deformation theory and Grothendieck's algebraic deformation theory.
Study deformations of G2-instantons on nearly G2 manifolds.
problem Deformations of G2-instantons on nearly G2 manifolds.
method Formulated in terms of spinors and Dirac operators, proved isomorphism of infinitesimal deformations to kernel of an elliptic operator.
result Proved abelian instantons are rigid and described the deformation space of the canonical connection on specific nearly G2 manifolds.
Paper discusses conditions for deforming coupled Kähler-Einstein metrics.
problem Conditions for deforming coupled Kähler-Einstein metrics.
method Analyzes deformation of coupled Kähler-Einstein metrics on Fano manifolds.
result Necessary and sufficient condition for deformation of coupled Kähler-Einstein metrics.
Study of deformed Bott-Chern cohomology on complex manifolds.
problem Deformation theory and cohomology of complex manifolds.
method Introduce a double complex structure and study its Bott-Chern cohomology.
result Established a deformation theory for Bott-Chern cohomology and computed deformed cohomology for specific manifolds.
We prove several formulas related to Hodge theory and the Kodaira-Spencer-Kuranishi deformation theory of Kähler manifolds. As applications, we present a construction of globally convergent power series of integrable Beltrami differentials on Calabi-Yau manifolds and also a construction of global canonical family of ho…
In this paper we study the deformation theory of submanifolds characterized by a system of differential forms and provide a criterion for deformations of such submanifolds to be unobstructed. We apply this deformation theory to special Legendrian submanifolds in Sasaki-Einstein manifolds. In general, special Legendrian…
The paper proves formulas and theorems for J-Witten deformation on specific manifolds.
problem Analyzing J-Witten deformation on specific types of manifolds.
method Obtained a Lichnerowicz type formula and proved Kastler-Kalau-Walze type theorems.
result Proved the Kastler-Kalau-Walze type theorems for J-Witten deformation on 4D and 6D almost product spin manifolds.
In this article, we consider Cayley deformations of a compact complex surface in a Calabi--Yau four-fold. We will study complex deformations of compact complex submanifolds of Calabi--Yau manifolds with a view to explaining why complex and Cayley deformations of a compact complex surface are the same. We in fact prove …
Deformations of Dubrovin's Hurwitz Frobenius manifolds are constructed. The deformations depend on g(g+1)/2 complex parameters where g is the genus of the corresponding Riemann surface. In genus one, the flat metric of the deformed Frobenius manifold coincides with a metric associated with a one-parameter family of…
Study on deformations of special Lagrangians with boundary in Calabi-Yau manifolds.
problem Deformation problem for special Lagrangians with boundary constraints.
method Identifying tangent vectors with harmonic 1-forms vanishing on the boundary, proving unobstructed deformations.
result Moduli space of special Lagrangians with boundary is a smooth manifold.
Paper proves solutions for deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds.
problem Existence of solutions for deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds.
method Derive a priori estimates under the existence of an admissible C-subsolution; prove existence of solutions under the condition of existence of a supersolution. result Proves existence of solutions for the deformed Hermitian-Yang-Mills equation.
Extends deformation theory to higher-page analogues of manifolds.
problem Deformation theory of higher-page analogues of manifolds.
method Extends essential deformations from Iwasawa manifolds to page-1-∂∂-manifolds.
result Obtains an unobstructedness theorem for page-1-∂∂-manifolds.
The paper studies deformations of Calabi-Yau manifolds using Gauduchon metrics.
problem Deformations of Calabi-Yau manifolds under co-polarised conditions.
method Analyzes local deformations of Calabi-Yau ∂∂ˉ-manifolds using Gauduchon metrics and constructs a new hp-HS form. result Proves the p-SKT h-∂∂ˉ-property is deformation open. Study shows deformations of quaternionic Kähler manifolds are locally inhomogeneous.
problem Understanding deformations of quaternionic Kähler manifolds.
method Proved one-loop deformation of quaternionic Kähler manifolds are locally inhomogeneous.
result Full isometry group of one-loop deformations has cohomogeneity one.
Study on special metrics and deformations of solvmanifolds.
problem Existence and properties of Kähler metrics on solvmanifolds.
method Investigation of strong Kähler with torsion metrics and balanced metrics on deformations of specific solvmanifolds.
result Non-existence of certain metrics on specific solvmanifolds.
Extending the work of G. Székelyhidi and T. Brönnle to Sasakian manifolds we prove that a small deformation of the complex structure of the cone of a constant scalar curvature Sasakian manifold admits a constant scalar curvature structure if it is K-polystable. This also implies that a small deformation of the complex …
Extends Cheeger's method to Lie groupoid actions on manifolds.
problem Smooth Lie group actions on manifolds with singularities.
method Extension of Cheeger's deformation techniques to Lie groupoid actions.
result Explicit sectional curvature description of the deformation.
Study instantons on asymptotically conical Spin(7)-manifolds, identifying deformation spaces.
problem Deformation theory of instantons on specific Spin(7)-manifolds.
method Relating deformation complex to spinors, identifying kernel of twisted negative Dirac operator.
result Virtual dimension of moduli space calculated using index theorem and Dirac operator spectrum.
Study on scalar curvature deformations in pseudohermitian manifolds.
problem Deformation of scalar curvature in pseudohermitian manifolds.
method Analogy with Riemannian manifolds, introduction of R-singular spaces, stability conditions, partial infinitesimal rigidity. result Partial infinitesimal rigidity result for scalar curvature of compact pseudohermitian manifolds.
The paper examines conditions for Kähler-Einstein metrics on deformations of Fano manifolds.
problem Conditions for Kähler-Einstein metrics on deformations of Fano manifolds.
method Analyzes necessary and sufficient conditions, approximates Weil-Petersson metric, describes plurisubharmonicity of energy functional.
result Provides new conditions for the existence of Kähler-Einstein metrics on deformations of Fano Kähler-Einstein manifolds.
This paper concerns with deformations of noncompact complex hyperbolic manifolds (with locally Bergman metric), varieties of discrete representations of their fundamental groups into PU(n,1) and the problem of (quasiconformal) stability of deformations of such groups and manifolds in the sense of L.Bers and D.Sulliva…
We define deformations of RP2-manifolds.
In this paper, we prove several formulas related to Hodge theory, and using them to prove the deformations of a compact H-twisted generalized Calabi-Yau manifold are unobstructed and L2 convergence in a neighborhood in another power series . And if we assume that the deformation is smooth in a fixed neighborhood, …
New findings on Frobenius structures on Kodaira manifolds.
problem Understanding Frobenius structures on Kodaira manifolds.
method Extended deformation theory and Frobenius structures.
result Frobenius structure on Kodaira manifolds is trivial on degree-2 component.
Study on non-orientable hyperbolic 3-manifolds and their deformations.
problem Understanding the deformation space of non-orientable hyperbolic 3-manifolds.
method Computing the deformation space of pairs (M^3, Δ) and determining representations in Isom(H^3).
result Existence of deformations not realizable as pair deformations.
Degenerate twistor deformations of Kähler manifolds are also Kähler.
problem Understanding the Kähler structure of degenerate twistor deformations.
method Using positive currents, Hahn–Banach theorem, and Huybrechts's theorem.
result Degenerate twistor deformations of compact holomorphically symplectic Kähler manifolds are Kähler.
Deformations of singular Cayley submanifolds studied.
problem Constructing fibrations of compact Spin(7) manifolds.
method Deformation theory of conically singular and asymptotically conical Cayley submanifolds.
result Detailed description of the deformation theory.
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…
We consider Lagrangian-like submanifolds in certain even-dimensional 'symplectic-like' Poisson manifolds. We show, under suitable transversality hypotheses, that the pair consisting of the ambient Poisson manifold and the submanifold has unobstructed deformations and that the deformations automatically preserve the Lag…
Study on new metrics on para-Kähler-Norden manifolds with conformal deformation.
problem Exploring geometric and harmonic properties of new metrics.
method Conformal deformation of Berger-type metric, analysis of Levi-Civita link, study of curvature varieties, and harmonic maps.
result Detailed examination of curvature varieties and harmonic maps on the manifold.
Study on symplectic structures and their deformations.
problem Preservation of complex symplectic structures under deformations.
method Analyzes various cohomologies and conditions for deformations.
result Obtains topological obstructions for compact complex symplectic manifolds.
Deformations of a Courant Algebroid E and its Dirac subbundle A have been widely considered under the assumption that the pseudo-Euclidean metric is fixed. In this paper, we attack the same problem in a setting that allows the pseudo-Euclidean metric to deform. Thanks to Roytenberg, a Courant algebroid is equivalent to…
We study infinitesimal Einstein deformations on compact flat manifolds and on product manifolds. Moreover, we prove refinements of results by Koiso and Bourguignon which yield obstructions on the existence of infinitesimal Einstein deformations under certain curvature conditions.
Stability of SKT metrics under deformations on complex manifolds.
problem Stability of strong Kähler with torsion metrics under small deformations.
method Finding necessary conditions for stability of SKT metrics along a family of complex manifolds.
result Necessary conditions for the stability of SKT metrics on a smooth curve of Hermitian metrics.