arXiv subjects

M. Ahmad Mirshafeazadeh

Publications and source records attributed to M. Ahmad Mirshafeazadeh.

2 recordsLinked to original sources

arXiv2026

Rigidity of complete non-compact generalized m-quasi-Einstein manifolds

We study complete non compact gradient generalized m quasi Einstein manifolds with constant scalar curvature R <= 0, soliton function lambda > 0, and m > 1, where the coefficient mu = 1/m is constant. We introduce the weighted function v and prove it is subharmonic. This leads to four rigidity results, showing that the hypotheses are mutually inconsistent; consequently, no complete non compact gradient generalized m quasi Einstein manifold exists under the stated assumptions. We first show by a concrete example that if mu is allowed to be nonconstant, the rigidity conclusions fail even when all other hypotheses are satisfied. Therefore the constant mu condition is essential.

math.DG↗

arXiv2023

Harmonic vector fields and the Hodge Laplacian operator on Finsler geometry

We first present the natural definitions of the horizontal differential, the divergence (as an adjoint operator), and a $p$-harmonic form on a Finsler manifold. Next, we prove a Hodge-type theorem for a Finsler manifold in the sense that a horizontal $p$-form is harmonic if and only if the horizontal Laplacian vanishes. This viewpoint provides a new appropriate natural definition of harmonic vector fields in Finsler geometry. This approach leads to a Bochner-Yano type classification theorem based on the harmonic Ricci scalar. Finally, we show that a closed orientable Finsler manifold with a positive harmonic Ricci scalar has a zero Betti number.

math.DG↗