Clairaut conformal submersions

Meena, Kiran; Yadav, Akhilesh

doi:10.48550/arxiv.2202.00393

Cited by 2 publications

(3 citation statements)

References 12 publications

(13 reference statements)

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“…Let F : (M m , g) → (N n , h) be a conformal submersion between Riemannian manifolds. Then we have ( [10], Equation 3.27)…”

Section: Conformal Submersion From Ricci Solitonmentioning

confidence: 99%

Conformal submersions whose total manifolds admit a Ricci soliton

Meena¹,

Yadav²

2022

Preprint

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In this paper, we study conformal submersions from Ricci solitons to Riemannian manifolds. First, we study some properties of O' Neill tensor A, which are changed in the case of conformal submersion. We also find a necessary and sufficient condition for conformal submersion to be totally geodesic and calculate Ricci tensors for such map with different conditions. Further, we consider conformal submersion F : M → N from a Ricci soliton to a Riemannian manifold and obtain necessary conditions for fibers of F and base manifold N to be Ricci soliton, almost Ricci soliton and Einstein. Moreover, we find necessary conditions for a vector field and it's horizontal lift to be conformal on N and (KerF * ) ⊥ , respectively. Also, we calculate the scalar curvature of Ricci soliton M . Finally, we obtain a necessary and sufficient condition for F to be harmonic.

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“…Let F : (M m , g) → (N n , h) be a conformal submersion between Riemannian manifolds. Then we have ( [10], Equation 3.27)…”

Section: Conformal Submersion From Ricci Solitonmentioning

confidence: 99%

Conformal submersions whose total manifolds admit a Ricci soliton

Meena¹,

Yadav²

2022

Preprint

Self Cite

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“…In 1972, Bishop defined Clairaut Riemannian submersion with connected fibers and gave a necessary and sufficient condition for a Riemannian submersion to be Clairaut Riemannian submersion [4]. Further, Clairaut submersions were studied in [3], [7] and [8]. In [19] and [9], Clairaut Riemannian maps were introduced by using geodesic curve on the total and base spaces respectively, and obtained necessary and sufficient conditions for Riemannian maps to be Clairaut Riemannian maps.…”

Section: Introductionmentioning

confidence: 99%

“…A submersion π : P → Q is said to be a Clairaut submersion if there is a function ρ : P → R + such that for every geodesic, making an angle θ with the horizontal subspace then ρsinθ is constant. Further, Clairaut submersion has been studiedin [14] and in many other spaces viz. Lorentzian spaces, timelike and spacelike spaces [3,11,27,26].…”

Section: Introductionmentioning

confidence: 99%

Clairaut Anti-invariant Riemannian Maps from Kähler Manifolds

Yadav

Meena

2022

Mediterr. J. Math.

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In this paper, we define Clairaut semi-invariant Riemannian map F from a Riemannian manifold (M, g M ) to a Kähler manifold (N, g N , P ) with a non-trivial example. We find necessary and sufficient conditions for a curve on the base manifold of semi-invariant Riemannian map to be geodesic. Further, we obtain necessary and sufficient conditions for a semi-invariant Riemannian map to be Clairaut semi-invariant Riemannian map. Moreover, we find necessary and sufficient condition for Clairaut semi-invariant Riemannian map to be totally geodesic. In addition, we find necessary and sufficient condition for the distributions D1 and D2 of (kerF * ) ⊥ (which are arisen from the definition of Clairaut semi-invariant Riemannian map) to define totally geodesic foliation. Finally, we obtain necessary and sufficient conditions for (kerF * ) ⊥ and base manifold to be locally product manifold D1 × D2 and N (rangeF * ) × N (rangeF * ) ⊥ , respectively.

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Clairaut conformal submersions

Cited by 2 publications

References 12 publications

Conformal submersions whose total manifolds admit a Ricci soliton

Conformal submersions whose total manifolds admit a Ricci soliton

Clairaut Anti-invariant Riemannian Maps from Kähler Manifolds

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