Paper · Sep 14, 2026

K-contact manifolds admitting some geometric solitons with Semi-Symmetric Non-Metric Connection

Bidhan Mondal, Nirabhra Basu, Arindam Bhattacharyya

math.DGarXiv:2609.15147
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Abstract

In this paper, we introduce some type vector fields with respect to a semi-symmetric non-metric (SSNM) connection. We investigate several geometric properties of a K-contact manifold equipped with an SSNM connection and provide a concrete example to justify the relation between the scalar curvature of the SSNM connection and Levi-Civita connection that we have obtained in this paper. Furthermore, we have found the nature of Riemann solitons, conformal Ricci solitons and conformal -Ricci-Yamabe solitons on K-contact manifolds admitting a SSNM connection.\\ Finally, we determine the necessary and sufficient conditions for such a manifold to be -semi-symmetric, quasi-conformal-semi-symmetric and pseudo-projective-semi-symmetric.

Ricci solitonsAlmost & η-Ricci solitonsScalar curvatureSasakian & contact geometry

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Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper ∗-Ricci-Yamabe Soliton and Contact Geometry (Dibakar Dey, 2021)8Dey 2021 Kenmotsu metric as conformal η-Ricci soliton (Dipen Ganguly, 2021)6Ganguly 2021 Geometry of para-Sasakian metric as an almost conformal η-Ricci soliton (Sumanjit Sarkar, Santu Dey and Arindam Bhattacharyya, 2021)4Sarkar 2021 Nature of Some Solitons on Almost coKähler Manifolds and Asymptotically Harmonic Manifolds (Paritosh Ghosh, Hemangi Madhusudan Shah and Arindam Bhattacharyya, 2023)5Ghosh 2023 Einstein-type metrics and generalized Ricci solitons on weak f-K-contact manifolds (Vladimir Rovenski, 2023)7Rovenski 2023 Investigations on a Riemannian manifold with a semi-symmetric non-metric connection and gradient solitons (Krishnendu De, Uday Chand De and Aydin Gezer, 2024)3De 2024 Curvature tensors and hyperbolic solitons on Lorentzian trans-Sasakian space form (Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya, 2025)1Mondal 2025 Hyperbolic solitons on trans-Sasakian space forms and its submanifolds (Bidhan Mondal, Sibsankar Panda and Nirabhra Basu, 2026)2Mondal 2026
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    Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya PDF

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same authors Bidhan Mondal, Nirabhra Basu, Arindam Bhattacharyya · Shared terms “conformal Ricci”, “Civita connection”, “Levi Civita”

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    Bidhan Mondal, Sibsankar Panda and Nirabhra Basu PDF

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same authors Bidhan Mondal, Nirabhra Basu · Shared terms “Ricci Yamabe”, “Yamabe soliton”

  3. Investigations on a Riemannian manifold with a semi-symmetric non-metric connection and gradient solitons

    Krishnendu De, Uday Chand De and Aydin Gezer PDF

    Topics Almost & η-Ricci solitons, Scalar curvature, Ricci solitons · Shared terms “semi symmetric”, “metric connection”, “Yamabe soliton”

  4. Geometry of para-Sasakian metric as an almost conformal -Ricci soliton

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    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Scalar curvature · Same author Arindam Bhattacharyya · Shared terms “manifold admitting”, “vector field”

  5. Nature of Some Solitons on Almost coKähler Manifolds and Asymptotically Harmonic Manifolds

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    Topics Almost & η-Ricci solitons, Scalar curvature, Ricci solitons · Same author Arindam Bhattacharyya · Shared terms “manifold admitting”

  6. Kenmotsu metric as conformal -Ricci soliton

    Dipen Ganguly PDF

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “manifold admitting”, “vector field”, “relation”

  7. Einstein-type metrics and generalized Ricci solitons on weak -K-contact manifolds

    Vladimir Rovenski PDF

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Scalar curvature · Shared terms “sufficient conditions”, “vector field”

  8. -Ricci-Yamabe Soliton and Contact Geometry

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Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Ricci solitons Metrics that change under Ricci flow only by scaling and diffeomorphisms: shrinking, steady or expanding solitons. Start with: The Ricci flow on surfaces (Hamilton, 1988) Almost & η-Ricci solitons Variations on the Ricci soliton equation: let the constant λ become a function (almost solitons), add a term along a contact form (η-Ricci… Start with: Ricci almost solitons (Pigola et al., 2010) Scalar curvature The trace of the Ricci tensor. Under Ricci flow its minimum never decreases and positive scalar curvature (PSC) is preserved. Start with: On the proof of the positive mass conjecture in general relativity (Schoen et al., 1979) Sasakian & contact geometry Sasakian manifolds are odd-dimensional manifolds whose metric cone is Kähler. They carry a transverse Kähler structure, so Kähler–Ricci flow has an… Start with: THE SASAKI–RICCI FLOW (SMOCZYK et al., 2010)

In the guidebook

  1. 6C.4
    The Yamabe Problem and Critical ExponentsBook 6C · Nonlinear PDE: Variational and Geometric Methods

    Conformal changes of scalar curvature, the Yamabe functional, Aubin's threshold and Schoen's solution, concentration compactness and bubbles, and why Perelman's log-Sobolev minimisers always exist.

  2. 9B.6
    Scalar Curvature and TopologyBook 9B · Comparison, Convergence and Heat on Manifolds

    Positive scalar curvature, its obstructions, and the positive mass theorem.

  3. 11B.1
    Ricci SolitonsBook 11B · Solitons, Compactness and Singularities

    Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.