On warped product manifolds satisfying Ricci-Hessian class type equations

Sinem Güler; Sezgin Altay Demirbağ

doi:10.2298/PIM1817069G

On warped product manifolds satisfying Ricci-Hessian class type equations

Sinem Güler, Sezgin Altay Demirbağ

Department of Mathematics Engineering

Istanbul Technical University

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We deal with a study of warped product manifold which is also a generalized quasi Einstein manifold. Then, we investigate the relationships between such warped products and certain manifolds that provide some Ricci- Hessian type equations, such as Ric_f_m = λg for some smooth function λ, where Ric_f_m denotes the m-Bakery-Emery Ricci tensor. Finally, we obtain some rigidity conditions for such manifolds.

Original language	English
Pages (from-to)	69-75
Number of pages	7
Journal	Publications de l'Institut Mathematique
Volume	103
Issue number	117
DOIs	https://doi.org/10.2298/PIM1817069G
Publication status	Published - 2018

Bibliographical note

Publisher Copyright:
© 2018, Mathematical Institute of the Serbian Academy of Sciences and Arts.

Funding

2010 Mathematics Subject Classification: 53C15; 53C25, 53B15. Key words and phrases: -Bakery–Emery Ricci tensor, generalized quasi Einstein manifold, warped product manifold, conformal vector field. This work is partially supported by the project BAP-38385 of Istanbul Technical University.

Funders	Funder number
Istanbul Technical University

Keywords

Conformal vector field
Generalized quasi Einstein manifold
Warped product manifold
m-Bakery-Emery Ricci tensor

Access to Document

10.2298/PIM1817069G

Cite this

@article{c2f06c3aa3ec48fb8cb0b3c8c2b78db4,

title = "On warped product manifolds satisfying Ricci-Hessian class type equations",

abstract = "We deal with a study of warped product manifold which is also a generalized quasi Einstein manifold. Then, we investigate the relationships between such warped products and certain manifolds that provide some Ricci- Hessian type equations, such as Ricfm = λg for some smooth function λ, where Ricfm denotes the m-Bakery-Emery Ricci tensor. Finally, we obtain some rigidity conditions for such manifolds.",

keywords = "Conformal vector field, Generalized quasi Einstein manifold, Warped product manifold, m-Bakery-Emery Ricci tensor",

author = "Sinem G{\"u}ler and Demirbağ, \{Sezgin Altay\}",

note = "Publisher Copyright: {\textcopyright} 2018, Mathematical Institute of the Serbian Academy of Sciences and Arts.",

year = "2018",

doi = "10.2298/PIM1817069G",

language = "English",

volume = "103",

pages = "69--75",

journal = "Publications de l'Institut Mathematique",

issn = "0350-1302",

publisher = "Mathematical Institute of the Serbian Academy of Sciences and Arts",

number = "117",

}

TY - JOUR

T1 - On warped product manifolds satisfying Ricci-Hessian class type equations

AU - Güler, Sinem

AU - Demirbağ, Sezgin Altay

PY - 2018

Y1 - 2018

N2 - We deal with a study of warped product manifold which is also a generalized quasi Einstein manifold. Then, we investigate the relationships between such warped products and certain manifolds that provide some Ricci- Hessian type equations, such as Ricfm = λg for some smooth function λ, where Ricfm denotes the m-Bakery-Emery Ricci tensor. Finally, we obtain some rigidity conditions for such manifolds.

AB - We deal with a study of warped product manifold which is also a generalized quasi Einstein manifold. Then, we investigate the relationships between such warped products and certain manifolds that provide some Ricci- Hessian type equations, such as Ricfm = λg for some smooth function λ, where Ricfm denotes the m-Bakery-Emery Ricci tensor. Finally, we obtain some rigidity conditions for such manifolds.

KW - Conformal vector field

KW - Generalized quasi Einstein manifold

KW - Warped product manifold

KW - m-Bakery-Emery Ricci tensor

UR - https://www.scopus.com/pages/publications/85047021053

U2 - 10.2298/PIM1817069G

DO - 10.2298/PIM1817069G

M3 - Article

AN - SCOPUS:85047021053

SN - 0350-1302

VL - 103

SP - 69

EP - 75

JO - Publications de l'Institut Mathematique

JF - Publications de l'Institut Mathematique

IS - 117

ER -

On warped product manifolds satisfying Ricci-Hessian class type equations

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this