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15 pages, 264 KB

Open AccessArticle

Geometry of Kenmotsu Manifolds via Q-Curvature Tensor and Schouten–Van Kampen Connection

by Mustafa Yıldırım, Selahattin Beyendi, Gülhan Ayar and Nesip Aktan

Axioms 2025, 14(7), 498; https://doi.org/10.3390/axioms14070498 - 26 Jun 2025

Cited by 1 | Viewed by 646

This research paper aims to study the Q-curvature tensor on Kenmotsu manifolds endowed with the Schouten–van Kampen connection. Using the Q-curvature tensor, whose trace is the well-known Z-tensor, we characterized Kenmotsu manifolds by introducing the notion of

ζ

\tilde{Q}

[...] Read more.

ζ

\tilde{Q}

flat and

ϕ

\tilde{Q}

flat manifolds and novel tensor conditions, such as

\tilde{Q} (ξ, X) \tilde{Q} = 0,

\tilde{Q} (ξ, X) \tilde{R} = 0,

\tilde{Q} (ξ, X) \tilde{C} = 0,

\tilde{Q} (ξ, X) \tilde{S} = 0

\tilde{Q} (ξ, X) \tilde{H} = 0

, and

\tilde{Q} (ξ, X) \tilde{P} = 0

, with the Schouten–van Kampen connection. To validate some of our results, we constructed a non-trivial example of Kenmotsu manifolds endowed with the Schouten–van Kampen connection. Full article

(This article belongs to the Special Issue Advances in Geometry and Its Applications)

20 pages, 363 KB

Open AccessArticle

Optimal Inequalities on (α,β)-Type Almost Contact Manifold with the Schouten–Van Kampen Connection

by Mohd Danish Siddiqi and Ali H. Hakami

Axioms 2023, 12(12), 1082; https://doi.org/10.3390/axioms12121082 - 27 Nov 2023

Cited by 5 | Viewed by 1719

Abstract

In the current research, we develop optimal inequalities for submanifolds in trans-Sasakian manifolds or

(α, β)

-type almost contact manifolds endowed with the Schouten–Van Kampen connection (

S V K

-connection), including generalized normalized

δ

-Casorati Curvatures (

δ

-CC). [...] Read more.

In the current research, we develop optimal inequalities for submanifolds in trans-Sasakian manifolds or

(α, β)

-type almost contact manifolds endowed with the Schouten–Van Kampen connection (

S V K

-connection), including generalized normalized

δ

-Casorati Curvatures (

δ

-CC). We also discuss submanifolds on which the equality situations occur. Lastly, we provided an example derived from this research. Full article

(This article belongs to the Special Issue Advances in Differential Geometry and Singularity Theory)

20 pages, 371 KB

Open AccessFeature PaperArticle

Quasi-Statistical Schouten–van Kampen Connections on the Tangent Bundle

by Simona-Luiza Druta-Romaniuc

Mathematics 2023, 11(22), 4614; https://doi.org/10.3390/math11224614 - 10 Nov 2023

Cited by 2 | Viewed by 1483

Abstract

We determine the general natural metrics G on the total space

T M

of the tangent bundle of a Riemannian manifold

(M, g)

such that the Schouten–van Kampen connection

\bar{\nabla}

associated to the Levi-Civita connection of G is (quasi-)statistical. [...] Read more.

We determine the general natural metrics G on the total space

T M

of the tangent bundle of a Riemannian manifold

(M, g)

such that the Schouten–van Kampen connection

\bar{\nabla}

associated to the Levi-Civita connection of G is (quasi-)statistical. We prove that the base manifold must be a space form and in particular, when G is a natural diagonal metric,

(M, g)

must be locally flat. We prove that there exist one family of natural diagonal metrics and two families of proper general natural metrics such that

(T M, \bar{\nabla}, G)

is a statistical manifold and one family of proper general natural metrics such that

(T M ∖ {0}, \bar{\nabla}, G)

is a quasi-statistical manifold. Full article

(This article belongs to the Special Issue Submanifolds in Metric Manifolds)

15 pages, 289 KB

Open AccessArticle

Biharmonic Maps on f-Kenmotsu Manifolds with the Schouten–van Kampen Connection

by Hichem El hendi

Mathematics 2023, 11(8), 1905; https://doi.org/10.3390/math11081905 - 17 Apr 2023

Cited by 2 | Viewed by 1471

Abstract

The object of the present paper was to study biharmonic maps on f-Kenmotsu manifolds and f-Kenmotsu manifolds with the Schouten–van Kampen connection. With the help of this connection, our results provided important insights related to harmonic and biharmonic maps. Full article

(This article belongs to the Special Issue Geometry of Manifolds and Applications)

11 pages, 283 KB

Open AccessArticle

Almost Paracontact Almost Paracomplex Riemannian Manifolds with a Pair of Associated Schouten–van Kampen Connections

by Hristo Manev and Mancho Manev

Mathematics 2021, 9(7), 736; https://doi.org/10.3390/math9070736 - 29 Mar 2021

Cited by 6 | Viewed by 1849

Abstract

Two correlated Schouten–van Kampen affine connections on an almost paracontact almost paracomplex Riemannian manifold are introduced and investigated. The considered manifolds are characterized by virtue of the presented non-symmetric connections. Curvature properties of the studied connections are obtained. A family of examples on [...] Read more.

(This article belongs to the Section B: Geometry and Topology)

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