Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold

Payel Karmakar

Mathematica Bohemica (2022)

  • Volume: 147, Issue: 3, page 419-434
  • ISSN: 0862-7959

Abstract

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The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, ξ -projectively flat, M -projectively flat, ξ - M -projectively flat, pseudo projectively flat and ξ -pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on Ricci flat, concircularly flat, M -projectively flat and pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting the aforesaid connection are studied. At last, some conclusions are made after observing all the results and an example of an anti-invariant submanifold of a trans-Sasakian manifold is given in which all the results can be verified easily.

How to cite

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Karmakar, Payel. "Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold." Mathematica Bohemica 147.3 (2022): 419-434. <http://eudml.org/doc/298474>.

@article{Karmakar2022,
abstract = {The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, $\xi $-projectively flat, $M$-projectively flat, $\xi $-$M$-projectively flat, pseudo projectively flat and $\xi $-pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on Ricci flat, concircularly flat, $M$-projectively flat and pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting the aforesaid connection are studied. At last, some conclusions are made after observing all the results and an example of an anti-invariant submanifold of a trans-Sasakian manifold is given in which all the results can be verified easily.},
author = {Karmakar, Payel},
journal = {Mathematica Bohemica},
keywords = {anti-invariant submanifold; trans-Sasakian manifold; Zamkovoy connection; $\eta $-Einstein manifold; Ricci curvature tensor; concircular curvature tensor; projective curvature tensor; $M$-projective curvature tensor; pseudo projective curvature tensor; Ricci soliton},
language = {eng},
number = {3},
pages = {419-434},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold},
url = {http://eudml.org/doc/298474},
volume = {147},
year = {2022},
}

TY - JOUR
AU - Karmakar, Payel
TI - Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold
JO - Mathematica Bohemica
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 147
IS - 3
SP - 419
EP - 434
AB - The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, $\xi $-projectively flat, $M$-projectively flat, $\xi $-$M$-projectively flat, pseudo projectively flat and $\xi $-pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on Ricci flat, concircularly flat, $M$-projectively flat and pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting the aforesaid connection are studied. At last, some conclusions are made after observing all the results and an example of an anti-invariant submanifold of a trans-Sasakian manifold is given in which all the results can be verified easily.
LA - eng
KW - anti-invariant submanifold; trans-Sasakian manifold; Zamkovoy connection; $\eta $-Einstein manifold; Ricci curvature tensor; concircular curvature tensor; projective curvature tensor; $M$-projective curvature tensor; pseudo projective curvature tensor; Ricci soliton
UR - http://eudml.org/doc/298474
ER -

References

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