T. Kashiwada and S. Tachibana defined conformal Killing p-forms on a Riemannian manifold of dimension 
$$m > p \geqslant 1$$

 and generalized some results on conformal Killing vector fields to the case of such forms. In this paper, conformal Killing p-forms are defined with the help of natural differental operators on Riemannian manifolds and representations of orthogonal groups. The geometry of the vector space 
$$T^p(M,\mathbb{R})$$

 of conformal Killing p-forms and of its two subspaces 
$$T^p(M,\mathbb{R})$$

 of coclosed conformal Killing p-forms and 
$$P^p(M,\mathbb{R})$$

 of closed conformal Killing p-forms are considered. Some local and global results due to Tachibana and Kashiwada about conformal Killing and Killing p-forms are generalized. An application to Hermitian geometry is given. Bibliography: 30 titles.

Integral formulas in riemannian geometry

The Vector Space of Conformal Killing Forms on a Riemannian Manifold

/pdf/infinitesimal-variations-of-submanifolds-1sjhjqug39.pdf

Infinitesimal variations of submanifolds

Abstract Let (M, g) be a non-Kenmotsu (κ, μ)′-almost Kenmotsu manifold of dimension 2n + 1. In this paper, we prove that if the metric g of M is a *-Ricci soliton, then either M is locally isometric to the product ℍn+1(−4)×ℝn or the potential vector field is strict infinitesimal contact transformation. Moreover, two concrete examples of (κ, μ)′-almost Kenmotsu 3-manifolds admitting a Killing vector field and strict infinitesimal contact transformation are given.

https://www.degruyter.com/document/doi/10.1515/math-2019-0056/pdf

*-Ricci soliton on (κ, μ)′-almost Kenmotsu manifolds

We find several sufficient conditions on a compact almost Ricci soliton under which it is a trivial Ricci soliton. We also find a sufficient condition under which a compact almost Ricci soliton is isometric to a sphere.

A note on almost Ricci solitons

Given a positive function F on S n which satisfies a convexity condition, we define the rth anisotropic mean curvature function M r for hypersurfaces in R n + 1 which is a generalization of the usual rth mean curvature function. Let X : M → R n + 1 be an n-dimensional closed hypersurface with M r + 1 M r = constant , for some r with 1 ⩽ r ⩽ n − 1 , which is a critical point for a variational problem. We show that X ( M ) is stable if and only if X ( M ) is the Wulff shape.

Integral formulas in riemannian geometry

Citations

The Vector Space of Conformal Killing Forms on a Riemannian Manifold

Infinitesimal variations of submanifolds

*-Ricci soliton on (κ, μ)′-almost Kenmotsu manifolds

A note on almost Ricci solitons

A new variational characterization of the Wulff shape

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