相关论文: d-objects kinematics on smooth manifolds

The task of shape abstraction with semantic part consistency is challenging due to the complex geometries of natural objects. Recent methods learn to represent an object shape using a set of simple primitives to fit the target.…

Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect…

In this work we define a deformation theory for the Coupled K\"ahler-Yang-Mills equations in arXiv:1102.0991, generalizing work of Sz\'ekelyhidi on constant scalar curvature K\"ahler metrics. We use the theory to find new solutions of the…

We introduce a natural notion of holomorphic map between generalized complex manifolds and we prove some related results on Dirac structures and generalized Kaehler manifolds.

Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental…

In this paper we study three-dimensional orbifolds by 2-groups with a trivially-acting one-form symmetry group BK. These orbifolds have a global two-form symmetry, and so one expects that they decompose into (are equivalent to) a disjoint…

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…

We give a general treatment of the master equation in homotopy algebras and describe the operads and formal differential geometric objects governing the corresponding algebraic structures. We show that the notion of Maurer-Cartan twisting…

This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of (0,-2)-curves on threefolds, or…

The universal deformation of the complex disk is studied from the viewpoint of infinite-dimensional geometry. The structure of a subsymmetric space on the universal deformation is described. The foliation of the universal deformation by…

One primary objective in submanifold geometry is to discover fascinating and significant classical examples of $H_1$. In this paper which relies on the theory we established in [Adv. Math. 405 (2022), 08514, 50 pages, arXiv:2101.11780] and…

This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields.…

A geodesic orbit manifold is a complete Riemannian manifold all of whose geodesics are orbits of one-parameter groups of isometries. We give both a geometric and an algebraic characterization of geodesic orbit manifolds that are…

The description of invariants of surfaces with respect to the motion groups is reduced to the description of invariants of parameterized surfaces with respect to the motion groups. Existence of a commuting system of invariant partial…

We outline the recent classification of differential structures for all main classes of quantum groups. We also outline the algebraic notion of `quantum manifold' and `quantum Riemannian manifold' based on quantum group principal bundles, a…

This paper lays the foundations for a nonlinear theory of differential geometry that is developed in a subsequent paper which is based on Colombeau algebras of tensor distributions on manifolds. We adopt a new approach and construct a…

The goal of this paper is to study the deformations of compact K\"ahler hyperbolic manifolds. We propose slightly modified versions of K\"ahler hyperbolicity as a tool to provide a first step towards investigating the deformation openness…

A notion of an algebroid - a generalization of a Lie algebroid structure is introduced. We show that many objects of the differential calculus on a manifold M associated with the canonical Lie algebroid structure on T^M can be obtained in…

Quantum general relativity may be considered as generally covariant QFT on differentiable manifolds, without any a priori metric structure. The kinematically covariance group acts by general diffeomorphisms on the manifold and by…

It is shown that a locally geometrical structure of arbitrarily curved Riemannian space is defined by a deformed group of its diffeomorphisms