P. Osipov

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20182026

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math.DG2026

Kunneth formula for Hessian manifolds

Pavel Osipov

We study Dolbeault--Koszul cohomology $H^{p, q} (M)$ of flat affine manifolds. We proove a Künneth formula \[ H^{p,q}(M\times N) \cong \bigoplus_{i,j} H^{i,j}(M)\otimes H^{p-i,q-j}(N…

math.DG2022

Locally conformally Hessian and statistical manifolds

Pavel Osipov

A statistical manifold $(M, D, g)$ is a manifold $M$ endowed with a torsion-free connection $D$ and a Riemannian metric $g$ such that the tensor $D g$ is totally symmetric…

math.DG2021

Statistical Lie algebras of a constant curvature and locally conformally Kähler Lie algebras

Pavel Osipov

We show that a statistical manifold manifold of a constant non-zero curvature can be realised as a level line of Hessian potential on a Hessian cone. We construct a Sasakian struct…

math.DG2020

Selfsimilar Hessian and conformally Kähler manifolds

Pavel Osipov

Let $(M, \nabla, g)$ be a Hessian manifold. Then the total space of the tangent bundle $T M$ can be endowed with a Kähler structure $(I, g)$ . We say that a homogeneou…

math.DG2019

Selfsimilar Hessian manifolds

Pavel Osipov

A selfsimiar manifold is a Riemannian manifold $(M, g)$ endowed with a homothetic vector field $ξ$ . We characterize global selfsimilar manifolds and describe the structur…

math.DG2018

Projective Hessian and Sasakian manifolds

Pavel Osipov

The Hessian geometry is the real analogue of the Kähler one. Sasakian geometry is an odd-dimensional counterpart of the Kähler geometry. In the paper, we study the connection betwe…