Alexander Petkov

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math.DG2025

Parallel torsion and $G_{2}, S p in (7)$ instantons

Stefan Ivanov, Alexander Petkov, Luis Ugarte

Instanton properties of the characteristic connection $\nabla$ on an integrable $G_{2}$ manifold as well as instanton condition of the torsion connection $\nabla$ on a $S p in (7)$ mani…

math.DG2025

The Riemannian curvature identities for the torsion connection on $S p in (7)$ -manifold and generalized Ricci solitons

Stefan Ivanov, Alexander Petkov

It is shown that on compact $S p in (7)$ --manifold with exterior derivative of the Lee form lying in the Lie algebra $s p in (7)$ the curvature $R$ of the $S p in (7)$ --torsion connection $…

math.DG2024

Li-Yau sub-gradient estimates and Perelman-type entropy formulas for the heat equation in quaternionic contact geometry

Stefan Ivanov, Alexander Petkov

We establish in the present paper two sub-gradient estimates for the quaternionic contact (qc) heat equation on a compact qc manifold of dimension $4 n + 3$ , provided some positivity…

Parallel torsion and G2​,Spin(7) instantons

The Riemannian curvature identities for the torsion connection on Spin(7)-manifold and generalized Ricci solitons

Li-Yau sub-gradient estimates and Perelman-type entropy formulas for the heat equation in quaternionic contact geometry

Parallel torsion and $G_{2}, S p in (7)$ instantons

The Riemannian curvature identities for the torsion connection on $S p in (7)$ -manifold and generalized Ricci solitons