arXiv research

The paper shows how to modify embeddings of $S^3$ without complex tangents.

We classify compact Kähler manifolds with semi-positive holomorphic bisectional and big tangent bundles. We also classify compact complex surfaces with semi-positive tangent bundles and compact complex $3$-folds of the form $P(T^*X)$ whose tangent bundles are nef. Moreover, we show that if $X$ is a Fano manifold such t…

Knots and links are shown to be complex tangents of a 3-sphere.

New complex structures found on tangent bundles of Lie groups.

Article proves tangent complex structure of Lie n-groupoid.

Researchers compute the cohomology of an elliptic tangent bundle.

Let $M$ be a close complex manifold and $TM$ its holomorphic tangent bundle. We prove that if the global holomorphic sections of tangent bundle generate each fibre, then $M$ is a complex homogeneous manifold. Our proof depends on the complex version of Chow-Rashevskii theorem in Carnot-Caratheodory spaces.

Complex functional maps link tangent bundles, preserving orientation and angles.

Embeddings of 3-manifolds into complex 3-space with specific tangents.

Paper proves unique tangent maps for complex maps into algebraic varieties.

Analytic sets with unique infinite tangent cone are algebraic.

The study identifies a topological barrier preventing the removal of certain complex tangents in 3-manifolds.

New Calabi-Yau metrics found on complex symmetric spaces.

Study minimal rational curves on complex manifolds with isotropic VMRT.

Classifies tangent cones of Kähler metrics with cone singularities.

We complete our recent classification of compact inner symmetric spaces with weakly complex tangent bundle by filling up a case which was left open, and extend this classification to the larger category of compact homogeneous spaces with positive Euler characteristic. We show that a simply connected compact equal rank …

Defines de Rham relative cotangent complex in tangent categories.

This paper explores differential and sector forms in tangent categories, finding rich structures and connections.

The paper classifies $\widetilde{J}$-tangent affine hyperspheres in arbitrary dimensions.

Extends T-duality to non-principal torus actions with elliptic tangent bundles.

Paper proves structure for compact Kähler manifolds with pseudo-effective tangent bundles.

Logarithmic connections on complex manifolds with trivial tangent bundle.

Paper calculates curvatures of metrics from isotropic structures.

Measures neural network complexity using tangent space diversity.

Abstracts connections in tangent categories, proving classical results.

Characterizes structures on generalized tangent bundles and CRF-structures.

Newlander-Nirenberg theorem extended to complex b-manifolds.

The paper proves structures for complex projective varieties with certain tangent bundle properties.

The abstract discusses classification theorems for complex contact manifolds and their geometric properties.

Reconstructs tangent bundle of complex projective plane using tropical geometry.

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.

Regularization effect found in neural feature alignment.

Generalizes complex manifolds to manifolds with corners and generalized corners.

The paper classifies 3D hypersurfaces with specific geometric properties.

The paper defines constraints for commuting endomorphisms in generalized tangent bundles.

The paper studies hyperkähler structures and adapted complex structures using the Monge-Ampère equation.

It is well-known that if a curve is a geodesic line of the tangent (sphere) bundle with Sasaki metric of a locally symmetric Riemannian manifold then the projected curve has all its geodesic curvatures constant. In this paper we consider the case of tangent (sphere) bundle over the real, complex and quaternionic space …

Study metallic structures on generalized tangent bundles.

Researchers found all invariant contact structures on tangent sphere bundles of compact symmetric spaces.

We prove that tangent cones to 2-dimensional calibrated cycles are unique. Using this result we prove a rate of convergence for the mass of the blow-up of a calibrated integral 2-cycle towards the limiting density. With the same techniques, we can also prove such a rate for J-holomorphic maps between almost complex man…

Study the intersection of positive closed currents using tangent currents and King's residue formula.

Paper explores complex tangencies to embeddings of S³ into C³.

We consider positive-(1,1) De Rham currents in arbitrary almost complex manifolds and prove the uniqueness of the tangent cone at any point where the density does not have a jump with respect to all of its values in a neighbourhood. Without this assumption, counterexamples to the uniqueness of tangent cones can be prod…

An explanation is given for the initially surprising ubiquity of separating sets in normal complex surface germs. It is shown that they are quite common in higher dimensions too. The relationship between separating sets and the geometry of the metric tangent cone of Bernig and Lytchak is described. Moreover, separating…

Study characterizes totally geodesic submanifolds in quotient spaces.

In this paper we define and study pseudoholomorphic vector bundles structures, particular cases of which are tangent and normal bundle almost complex structures. These are intrinsically related to the Gromov D-operator. As an application we deduce normal forms of 1-jets of almost complex structures along a submanifold.…

We define a class of metrics that extend the Sasaki metric of a tangent manifold of a Riemannian manifold. The new metrics are obtained by the transfer of the generalized (pseudo-)Riemannian metrics of the pullback of the big tangent bundle of a manifold to the tangent manifold. We obtain the expression of the transfer…

Study complex structures with totally real sections, providing integrability equations.