Shubham Dwivedi

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math.DG2026

Ricci flow with metric torsion on surfaces of positive Euler characteristic

Shubham Dwivedi

We study an adapted Ricci flow of connections with metric torsion on surfaces with positive Euler characteristic. We first prove that there do not exist any nontrivial solitons of…

math.DG2026

A $d d^{Φ}$ -Lemma and Bott--Chern-type Cohomology for Spin(7)-Manifolds

Shubham Dwivedi, Ragini Singhal

We study the properties of the $d d^{Φ}$ -operator on $8$ -dimensional Spin(7)-manifolds with torsion-free Spin(7)-structures $Φ$ . These operators were first introduced by Harvey and La…

math.DG2026

Solutions and singularities of the Ricci-harmonic flow and Ricci-like flows of $G_{2}$ -structures

Shubham Dwivedi, Ragini Singhal

We find explicit solutions and singularities of the Ricci-harmonic flow of $G_{2}$ -structures, the Ricci-like flows of $G_{2}$ -structures studied by Gianniotis-Zachar…

math.DG2026

Ricci-harmonic flow of $G_{2}$ and Spin(7)-structures

Shubham Dwivedi

We introduce and study a new general flow of $G_{2}$ -structures which we call the Ricci-harmonic flow of $G_{2}$ -structures. The flow is the coupling of the Ricci flo…

math.DG2023

Flows of $G_{2}$ -structures, II: Curvature, torsion, symbols, and functionals

Shubham Dwivedi, Panagiotis Gianniotis, Spiro Karigiannis

We continue the investigation of general geometric flows of $G_{2}$ -structures initiated by the third author in "Flows of $G_{2}$ -structures, I." Specifically, we determine the possibl…

Ricci flow with metric torsion on surfaces of positive Euler characteristic

A ddΦ-Lemma and Bott--Chern-type Cohomology for Spin(7)-Manifolds

Solutions and singularities of the Ricci-harmonic flow and Ricci-like flows of G2​-structures

Ricci-harmonic flow of G2​ and Spin(7)-structures

Flows of G2​-structures, II: Curvature, torsion, symbols, and functionals

A $d d^{Φ}$ -Lemma and Bott--Chern-type Cohomology for Spin(7)-Manifolds

Solutions and singularities of the Ricci-harmonic flow and Ricci-like flows of $G_{2}$ -structures

Ricci-harmonic flow of $G_{2}$ and Spin(7)-structures

Flows of $G_{2}$ -structures, II: Curvature, torsion, symbols, and functionals