arXiv research

For a representation of a finite group $G$ on a complex vector space $V$ we determine when a holomorphic $\binom{p}{q}$-tensor field on the principle stratum of the orbit space $V/G$ can be lifted to a holomorphic $G$-invariant tensor field on $V$. This extends also to connections. As a consequence we determine those h…

Vanishing theorems show holomorphic tensor fields on certain Kähler manifolds are trivial.

Holomorphic tensors on Vaisman manifolds are invariant under the Lee field.

Vanishing theorem for certain tensor fields on compact Hermitian manifolds.

Holomorphic tensors on algebraic cones are invariant under certain group actions.

We prove the existence of non-positively curved Kähler-Einstein metrics with cone singularities along a given simple normal crossing divisor on a compact Kähler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved Kähler-Einstein metrics with cone singularities. As…

Introduces compatibility between Dirac structures and Nijenhuis tensors.

The properties of Kaehler submanifolds with recurrent the second fundamental form in spaces of constant holomorphic sectional curvature are being studied in this article.

We study in a uniform manner the properties of biconservative surfaces in arbitrary Riemannian manifolds. Biconservative surfaces being characterized by the vanishing of the divergence of a symmetric tensor field $S_2$ of type $(1,1)$, their properties will follow from general properties of a symmetric tensor field of …

The paper explores conditions for real holomorphic gradient fields on Kähler and conformally Kähler manifolds.

We establish a Penrose-Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor space, we derive sets of manifestly N=(1,0) and N=(2,0) supersymmetric non-Abeli…

We study tensors on Lie groupoids suitably compatible with the groupoid structure, called {\em multiplicative}. Our main result gives a complete description of these objects only in terms of infinitesimal data. Special cases include the infinitesimal counterparts of multiplicative forms, multivector fields and holomorp…

New proof shows holomorphic sectional curvature fully determines curvature tensor.

In this paper we introduce a new algebraic device, which enables us to treat the quaternions as though they were a commutative field. This is of interest both for its own sake, and because it can be applied to develop an "algebraic geometry" of noncompact hypercomplex manifolds. The basic building blocks of the theory …

We study complex 4-manifolds with holomorphic self-dual conformal structures, and we obtain an interpretation of the Weyl tensor of such a manifold as the projective curvature of a field of cones on the ambitwistor space. In particular, its vanishing is implied by the existence of some compact, simply-connected, null-g…

Solves a Monge-Ampère type equation for Nakano positive curvature tensors of holomorphic vector bundles.

The study characterizes symmetries in Kaehler manifolds.

Paper solves tensor problem for holomorphic vector bundles.

Let $M$ be a real hypersurface of a complex space form $M^n(c)$, $c\neq0$, $n\geq 3$. We show that the Ricci tensor $S$ of $M$ satisfies $S(X,Y)=ag(X,Y)$ for any vector fields $X$ and $Y$ on the holomorphic distribution, $a$ being a constant, if and only if $M$ is a pseudo-Einstein real hypersurface.

The paper explores symmetries in Kähler manifolds using Ricci tensor properties.

This paper deals with sheaves of differential operators on noncommutative algebras. The sheaves are defined by quotienting a the tensor algebra of vector fields (suitably deformed by a covariant derivative) to ensure zero curvature. As an example we can obtain enveloping algebra like relations for Hopf algebras with di…

The following result is proved: Consider a 4-dimensional Kaehler manifold M with nonvanishing Bochner tensor B. Then any holomorphic transformation of M, which preserves B is a homothety.

Study optimal holomorphic extensions for jets along submanifolds as tensor powers increase.

We study some analytical and geometric properties of a two-dimensional nonlinear sigma model with gravitino which comes from supersymmetric string theory. When the action is critical w.r.t. variations of the various fields including the gravitino, there is a symmetric, traceless and divergence-free energy-momentum tens…

Let (M,g) be a pseudo-Riemannian manifold and $T^2M$ be its the second-order tangent bundle equipped with the deformed 2-nd lift metric g which obtained from the 2-nd lift metric by deforming the horizontal part with a symmetric (0,2)-tensor field c. In the present paper, we first compute the Levi-Civita connection and…

Study of $H$-eigenvalues for complex tensors and their applications in differential geometry.

Paper describes holomorphic polyvector fields on toric varieties.

Study calculates curvatures in holomorphic fibrations using degenerate Hermitian forms.

In this paper, we introduce the stress-energy tensors of the partial energies E'(f) and E"(f) of maps between Kaehler manifolds. Assuming the domain manifolds poss some special exhaustion functions, we use these stress-energy tensors to establish some monotonicity formulae of the partial energies of pluriharmonic maps …

Study BV operators on holomorphic polyvector fields on toric varieties.

We prove a general uniformization theorem for N=2 superconformal and N=1 superanalytic DeWitt super-Riemann surfaces, showing that in general an N=2 superconformal (resp. N=1 superanalytic) DeWitt super-Riemann surface is N=2 superconformally (resp., N=1 superanalytically) equivalent to a manifold with transition funct…

In this paper we study numerical properties of quotients of holomorphic log-tensors.

Study finds conditions for minimum of Donaldson's functional on Higgs bundles with non-holomorphic Higgs fields.

The paper studies quarter-symmetric connections on Hermitian and Kähler manifolds.

Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.

The goal of this paper is to study the theory of last multipliers in the framework of complex manifolds with a fixed holomorphic volume form. The motivation of our study is based on the equivalence between a holomorphic ODE system and an associated real ODE system and we are interested how we can relate holomorphic las…

The paper studies distributions on surfaces and their connection to twistor spaces.

Researchers found indecomposable Killing tensor fields on quaternionic projective spaces.

Let X be a Kähler manifold and D be a R-divisor with simple normal crossing support and coefficients between 1/2 and 1. Assuming that K_X+D is ample, we prove the existence and uniqueness of a negatively curved Kahler-Einstein metric on X\D having mixed Poincaré and cone singularities according to the coefficients of D…

The paper classifies Killing tensor fields on Riemannian symmetric spaces.

We prove that a compact lcK manifold with holomorphic Lee vector field is Vaisman provided that either the Lee field has constant norm or the metric is Gauduchon (i.e., the Lee field is divergence-free). We also give examples of compact lcK manifolds with holomorphic Lee vector field which are not Vaisman.

The paper proves the existence of a complete holomorphic vector field on a complex manifold with a Kähler-Einstein metric.

We find the entropy's infinite-size behavior in complex manifold sections.

Killing fields on compact pseudo-Kähler manifolds are holomorphic.

Study asymptotics of extension and orthogonal Bergman kernels for high tensor powers of positive line bundles.

The paper proves UV finiteness and vanishing anomalies for hybrid topological-holomorphic field theories.

Conformal vector fields on lcK manifolds are shown to be Killing or holomorphic.

A symmetric tensor field on a Riemannian manifold is called Killing field if the symmetric part of its covariant derivative is equal to zero. There is a one to one correspondence between Killing tensor fields and first integrals of the geodesic flow which depend polynomially on the velocity. Therefore Killing tensor fi…