Biconservative Surfaces in Robertson–Walker Spaces

Nurettin Cenk Turgay; Rüya Yeǧin Şen

doi:10.1007/s00025-025-02395-5

Biconservative Surfaces in Robertson–Walker Spaces

Nurettin Cenk Turgay^*, Rüya Yeǧin Şen

^*Corresponding author for this work

Department of Mathematics Engineering

Istanbul Medeniyet University

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

Abstract

In this paper, we mainly focus on space-like PMCV surfaces in Robertson–Walker spaces. First, we derive certain geometrical properties of biconservative surfaces in the Robertson–Walker space L1n(f,c) of arbitrary dimension. Then, we get complete local classifications of PMCV surfaces in L14(f,0), L15(f,0) and L15(1,±1). Finally, we prove that a space-like PMCV biconservative surface in L1n(f,0),n≥6 lies on a totally geodesic submanifold with dimension either 4 or 5.

Original language	English
Article number	77
Journal	Results in Mathematics
Volume	80
Issue number	3
DOIs	https://doi.org/10.1007/s00025-025-02395-5
Publication status	Published - May 2025

Bibliographical note

Publisher Copyright:
© The Author(s) 2025.

Keywords

53A10 (Primary)
53C42
Biharmonic surfaces
Parallel mean curvature vector
Robertson–Walker spacetime

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10.1007/s00025-025-02395-5

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title = "Biconservative Surfaces in Robertson–Walker Spaces",

abstract = "In this paper, we mainly focus on space-like PMCV surfaces in Robertson–Walker spaces. First, we derive certain geometrical properties of biconservative surfaces in the Robertson–Walker space L1n(f,c) of arbitrary dimension. Then, we get complete local classifications of PMCV surfaces in L14(f,0), L15(f,0) and L15(1,±1). Finally, we prove that a space-like PMCV biconservative surface in L1n(f,0),n≥6 lies on a totally geodesic submanifold with dimension either 4 or 5.",

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AU - Yeǧin Şen, Rüya

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PY - 2025/5

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N2 - In this paper, we mainly focus on space-like PMCV surfaces in Robertson–Walker spaces. First, we derive certain geometrical properties of biconservative surfaces in the Robertson–Walker space L1n(f,c) of arbitrary dimension. Then, we get complete local classifications of PMCV surfaces in L14(f,0), L15(f,0) and L15(1,±1). Finally, we prove that a space-like PMCV biconservative surface in L1n(f,0),n≥6 lies on a totally geodesic submanifold with dimension either 4 or 5.

AB - In this paper, we mainly focus on space-like PMCV surfaces in Robertson–Walker spaces. First, we derive certain geometrical properties of biconservative surfaces in the Robertson–Walker space L1n(f,c) of arbitrary dimension. Then, we get complete local classifications of PMCV surfaces in L14(f,0), L15(f,0) and L15(1,±1). Finally, we prove that a space-like PMCV biconservative surface in L1n(f,0),n≥6 lies on a totally geodesic submanifold with dimension either 4 or 5.

KW - 53A10 (Primary)

KW - 53C42

KW - Biharmonic surfaces

KW - Parallel mean curvature vector

KW - Robertson–Walker spacetime

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JO - Results in Mathematics

JF - Results in Mathematics

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ER -

Biconservative Surfaces in Robertson–Walker Spaces

Abstract

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Keywords

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