CMC biconservative surfaces in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">S</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup><mml:mo>×</mml:mo><mml:mi mathvariant="double-struck">R</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">H</mml:mi></mml:mrow><mml:mrow><m

Fetcu, Dorel; Oniciuc, Cezar; Pinheiro, Ana Lucia

doi:10.1016/j.jmaa.2014.12.051

Cited by 29 publications

(35 citation statements)

References 27 publications

(26 reference statements)

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“…The class of biconservative submanifolds includes that of biharmonic submanifolds, which have been of great interest in the last decade . It is well known that ψ is biconservative if and only if

{m \nabla ∥ H ∥}^{2} + 4 trace S_{\nabla_{\cdot}^{⊥} H} false(\cdot false) + 4 trace {(\tilde{R} false(\cdot, H false) \cdot)}^{T} = 0,

where H ,

\nabla^{⊥}

, S are the mean curvature, the normal connection, the shape operator of M , respectively and

\overset{R}{true}

is the curvature tensor of N .…”

Section: Introductionmentioning

confidence: 99%

On biconservative hypersurfaces in ‐dimensional Riemannian space forms

Turgay

Upadhyay

2019

Mathematische Nachrichten

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{m \nabla ∥ H ∥}^{2} + 4 trace S_{\nabla_{\cdot}^{⊥} H} false(\cdot false) + 4 trace {(\tilde{R} false(\cdot, H false) \cdot)}^{T} = 0,

where H ,

\nabla^{⊥}

, S are the mean curvature, the normal connection, the shape operator of M , respectively and

\overset{R}{true}

is the curvature tensor of N .…”

Section: Introductionmentioning

confidence: 99%

On biconservative hypersurfaces in ‐dimensional Riemannian space forms

Turgay

Upadhyay

2019

Mathematische Nachrichten

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“…In particular, they gave a complete classification of biconservative surfaces with constant mean curvature in Euclidean 4-space. Very recently, Fetcu et al classified biconservative surfaces with parallel mean curvature vector field in product spaces S n × R and H n × R in [13].…”

Section: Introductionmentioning

confidence: 99%

Complete classification of biconservative hypersurfaces with diagonalizable shape operator in the Minkowski 4-space

Turgay

2016

Int. J. Math.

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“…The spacelike and timelike biconservative hypersurfaces of the three‐dimensional Minkowski space were studied in , where the author gave the local parametrization of the biconservative surfaces that do not have constant mean curvature. Also, in , the authors present the classification of the non minimal biconservative surfaces, with parallel mean vector field, in the product spaces

{double-struckS}^{n} \times R

and

{double-struckH}^{n} \times R

. In there is a motivating study of the relationship between biconservative surfaces and the holomorphicity of a generalized Hopf function.…”

Section: Introductionmentioning

confidence: 99%

Biconservative surfaces in BCV‐spaces

Montaldo

Onnis²,

Passamani³

2017

Mathematische Nachrichten

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Abstract. Biconservative hypersurfaces are hypersurfaces with conservative stress-energy tensor with respect to the bienergy functional, and form a geometrically interesting family which includes that of biharmonic hypersurfaces. In this paper we study biconservative surfaces in the 3-dimensional Bianchi-Cartan-Vranceanu spaces, obtaining their characterization in the following cases: when they form a constant angle with the Hopf vector field; when they are SO(2)-invariant.

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CMC biconservative surfaces in Sn×R and H

Cited by 29 publications

References 27 publications

On biconservative hypersurfaces in ‐dimensional Riemannian space forms

On biconservative hypersurfaces in ‐dimensional Riemannian space forms

Complete classification of biconservative hypersurfaces with diagonalizable shape operator in the Minkowski 4-space

Biconservative surfaces in BCV‐spaces

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