arXiv research

The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the properties and specific features of the differential-geometrical structures. The…

Study geometric properties of cuspidal edges with boundary.

Differential geometry applied to Mukai duality on K3 surfaces.

The paper shows how to learn the geometric structure of data manifolds using probabilistic methods.

This work proposes a geometric approach to identify slow invariant manifolds in dynamical systems.

Study dualities of geometric invariants on cuspidal edges in hyperbolic and de Sitter spaces.

Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (with unclosed metric forms). Such forms possess a peculiarity, namely, the closed inexact exterior forms are obtained from that. The closur…

The differential geometric aspects of Geometric Phases are reviewed.

Study geometric properties of S1 singularities and their deformations.

The exposition has been significantly altered, hopefully improved.

Study classifies Hamiltonian operators with skew-symmetric constraints.

Differential geomtrical methods for deriving the Dirac equation in Curved Spacetime are presented. Einstein's field equation is applied in a novel manner; in the most current standard reference, Birrell and Davies, 1994 [1], the suggestions for deriving the Dirac equation in Curved Spacetime make no mention of employin…

The paper simplifies FLRW photon propagators using geometric embeddings.

We simplify complex geometric structures for contracting measurable systems.

In this paper, we give a geometric expression for the multiplicities of the equivariant index of a spin-c Dirac operator.

Advances M-polyfolds for complex geometry applications.

Classifies third-order Hamiltonian operators based on algebraic variety properties.

This note shows the compatibility of the differential geometric and the topological formulations of equivariant characteristic classes for a compact connected Lie group action.

Smooth complex surfaces with triple intersections using differential geometry.

Variational approach to basic manifold structures.

Purely real space versions of the differential equations describing the kinematics of a dislocated crystalline medium are considered. The differential geometric structures associated with them are revealed.

The purpose of the present paper is to study the differential geometric properties of a quaternion CR-submanifold in a locally conformal quaternion Kaehler manifold.

In this paper we investigate the differential geometric and algebro-geometric properties of the noncollapsing limit in the continuity method that was introduced by the first two named authors in \cite{LaTi14}.

We give a differential geometric description of the Cartan (or tractor) bundle and its canonical connection in CR geometry, thus offering a direct, alternative, definition to the usual abstract approach.

This article gives an exposition of the deformation theory for pairs $(X, E)$, where $X$ is a compact complex manifold and $E$ is a holomorphic vector bundle over $X$, adapting an analytic viewpoint à la Kodaira-Spencer. By introducing and exploiting an auxiliary differential operator, we derive the Maurer--Cartan equa…

This paper generalizes Batchelor's theorem in $C^\infty$-superschemes.

Certain solutions of a sextic sigma-model Lagrangian reminiscent of Skyrme model correspond to perfect fluids with stiff matter equation of state. We analyse from a differential geometric perspective this correspondence extended to general barotropic fluids.

In this paper, Hamiltonian monodromy is studied from the point of view of geometric quantization abd theta functions, and various differential geometric aspects thereof are dealt with, all related to holonomies of suitable flat connections.

Paper proves existence of conjugate points on ellipsoids but not on spheres.

Study of lightcone framed surfaces in Lorentz-Minkowski 3-space, focusing on curvature behavior.

Study conical Kahler metrics, focusing on limits and equations.

MATLAB toolbox pde2path solves geometric PDEs and finds bifurcations in immersed surfaces.

A second order variational description of the autoparallel curves of some differential-geometric connection for the third order Mathisson's 'new mechanics' of a relativistic free spinning particle is suggested starting from general requirements of invariance and 'variationality'.

The paper classifies diffeomorphism classes of Calabi-Yau threefolds constructed by gluing methods.

Study the geometry of lightlike loci on mixed type surfaces in Lorentz-Minkowski 3-space.

In this paper, we introduce a new concept so called harmonic complex structure by using harmonic theory for vector bundle-valued differential forms. It is a new structure intermediates between complex structure and Kähler structure. From differential geometric viewpoint, it is a natural generalization of Kähler structu…

In this paper, we explore the virtual technique that is very useful in studying moduli problem from differential geometric point of view. We introduce a class of new objects "virtual manifolds/orbifolds", on which we develop the integration theory. In particular, the virtual localization formula is obtained.

We give a normal form of the cuspidal edge which uses only diffeomorphisms on the source and isometries on the target. Using this normal form, we study differential geometric invariants of cuspidal edges which determine them up to order three. We also clarify relations between these invariants.

Introduces non-regular spacetime geometry without smooth calculus.

We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation. We prove the appropriate generalizations of Bochner--Weitzenböck formula and Laplacian comparison theorem, and study the h…

Bour's minimal surface has remarkable properties in three dimensional Minkowski space. We reveal the definite and indefinite cases of the Bour's surface using Weierstrass representations, and give some differential geometric properties of the astonishing maximal and minimal surfaces.

We apply a local differential geometric framework from Kähler toric geometry to (re)construct Calabi's extremal Kähler metrics on $\bbC\bbP^n$ blown-up at a point from data on the moment polytope.

We define a new kind of helicoidal surface of value m. A rotational surface which is isometric to the helicoidal surface of value m is revealed. In addition, we calculate some differential geometric properties of the helicoidal surface of value 3 in three dimensional Euclidean space.

The goal of this paper is to introduce the lifting theory that has an important role in geometry. Therefore, using the lifts of differential geometric structures we show that tangent bundle TM of paracomplex manifold M admits para-complex torsion-free affine connection.

In this paper, we start from an extension of the notion of holonomy on diffeological bundles, reformulate the notion of regular Lie group or Frölicher Lie groups, state an Ambrose-Singer theorem that enlarges the one stated in \cite{Ma2}, and conclude with a differential geometric treatment of KP hierarchy. The example…

The paper mostly collects material on generic rank of $A$--modules with respect to differential geometric applications. Our research was motivated by geometry of $A$--structures. In particular, we discuss the case where $A$ is an unitary associative algebra not necessary with inversion. Some of the examples are studied…

In this paper, by using the Kuranishi coordinates on the Teichmüller space and the explicit deformation formula of holomorphic one-forms on Riemann surface, we give an explicit expression of the period map and derive new differential geometric proofs of the Torelli theorems, both local and global, for Riemann surfaces.

Geometric families of low-rank covariances improve flexibility and tractability in high dimensions.