Classification of base of warped product almost Ricci solitons

Autor:	Gomes, José N. V., Neto, Manoel V. M.
Rok vydání:	2017
Předmět:	Mathematics - Differential Geometry Primary 53C15 53A30 Secondary 53C24 53C12
Druh dokumentu:	Working Paper
Popis:	In this paper we study a Ricci-Hessian type manifold $(\Bbb{M},g,\varphi,f,\lambda)$ which is closely related to the construction of almost Ricci soliton realized as a warped product. We classify certain classes of the Ricci-Hessian type manifolds and derive some implications for almost Ricci solitons and generalized $m$--quasi-Einstein manifolds. We consider two complementary cases: $\nabla f$ and $\nabla\varphi$ are linearly independent in $C^\infty(\Bbb{M})$--module $\mathfrak{X}(\Bbb{M})$; and $\nabla f=h\nabla\varphi$ for a smooth function $h$ on $\Bbb{M}$. In the first case we show that the vector field $\nabla\lambda$ belongs to the $C^\infty(\Bbb{M})$--module generated by $\nabla f$ and $\nabla\varphi$, while in the second case, under additional hypothesis, the manifold is, around any regular point of $f$, locally isometric to a warped product. Comment: 18 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1704.03130 Zobrazit plný text záznamu View this record from Arxiv