Paper · Jul 17, 2017

Invariant submanifolds of generalized Sasakian-space-forms

Shyamal Kumar Hui, Siraj Uddin, Ali H. Alkhaldi, Pradip Mandal

math.DGarXiv:1707.04985
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Abstract

The present paper deals with the study of invariant submanifolds of generalized Sasakian-space-forms with respect to Levi-Civita connection as well as semi-symmetric metric connection. We provide some examples of such submanifolds and obtain many new results including, the necessary and sufficient conditions under which the submanifolds are totally geodesic. The Ricci solitons of such submanifolds are also studied.

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Submitted
Jul 17, 2017
Subjects
math.DG
DOI
10.1142/S0219887818501499

Comments: 20 pages. The authors invites suggestions / comments from interested researchers for the improvement of the paper

Ricci solitonsSphere theoremsSasakian & 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 Solitons on submanifolds of (LCS)ₙ-Manifolds (Shyamal Kumar Hui, Rajendra Prasad and Tanumoy Pal, 2017)3Hui 2017 Invariant and anti-invariant submanifolds of special quasi-sasakian manifolds (Shyamal Kumar Hui and Joydeb Roy, 2017)1Hui 2017 *-Conformal η-Ricci Soliton on Sasakian manifold (Soumendu Roy, Santu Dey, Arindam Bhattacharyya et al., 2019)6Roy 2019 Sasakian immersions of Sasaki-Ricci solitons into Sasakian space forms (Giovanni Placini, 2021)2Placini 2021 Immersions of Sasaki-Ricci solitons into homogeneous Sasakian manifolds (Roberto Mossa and Giovanni Placini, 2023)7Mossa 2023 Curvature tensors and hyperbolic solitons on Lorentzian trans-Sasakian space form (Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya, 2025)4Mondal 2025 Hyperbolic solitons on trans-Sasakian space forms and its submanifolds (Bidhan Mondal, Sibsankar Panda and Nirabhra Basu, 2026)5Mondal 2026 K-contact manifolds admitting some geometric solitons with Semi-Symmetric Non-Metric Connection (Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya, 2026)8Mondal 2026
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  1. Invariant and anti-invariant submanifolds of special quasi-sasakian manifolds

    Shyamal Kumar Hui and Joydeb Roy

    Topics Sasakian & contact geometry, Ricci solitons · Same author Shyamal Kumar Hui · Shared terms “invariant submanifolds”, “Civita connection”, “Levi Civita”

  2. Sasakian immersions of Sasaki-Ricci solitons into Sasakian space forms

    Giovanni Placini

    Topics Sasakian & contact geometry, Sphere theorems, Ricci solitons · Shared terms “Sasakian space”, “space form”

  3. Ricci Solitons on submanifolds of -Manifolds

    Shyamal Kumar Hui, Rajendra Prasad and Tanumoy Pal

    Topics Ricci solitons · Same author Shyamal Kumar Hui · Shared terms “invariant submanifolds”, “symmetric metric”, “metric connection”

  4. Curvature tensors and hyperbolic solitons on Lorentzian trans-Sasakian space form

    Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya

    Topics Sasakian & contact geometry, Sphere theorems, Ricci solitons · Shared terms “Sasakian space”, “space form”, “Civita connection”

  5. Hyperbolic solitons on trans-Sasakian space forms and its submanifolds

    Bidhan Mondal, Sibsankar Panda and Nirabhra Basu

    Topics Sasakian & contact geometry, Sphere theorems, Ricci solitons · Shared terms “Sasakian space”, “space form”

  6. *-Conformal η-Ricci Soliton on Sasakian manifold

    Soumendu Roy, Santu Dey, Arindam Bhattacharyya et al.

    Topics Sasakian & contact geometry, Ricci solitons · Same author Shyamal Kumar Hui

  7. Immersions of Sasaki-Ricci solitons into homogeneous Sasakian manifolds

    Roberto Mossa and Giovanni Placini

    Topics Sasakian & contact geometry, Sphere theorems, Ricci solitons · Shared terms “Sasakian space”, “space form”

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

    Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “semi symmetric”, “metric connection”, “Civita connection”

Read around it

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) Sphere theorems Curvature conditions that force a manifold to be a sphere. Ricci flow settled the 1/4-pinched differentiable sphere theorem, which had been open for… Start with: Minimal Two-Spheres and the Topology of Manifolds with Positive Curvature on Totally Isotropic Two-Planes (Micallef et al., 1988) 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. 11A.11
    Hamilton’s 1982 TheoremBook 11A · The Ricci Flow: Existence and Maximum Principles

    Positive Ricci curvature in dimension 3 flows to a round metric.

  2. 11B.1
    Ricci SolitonsBook 11B · Solitons, Compactness and Singularities

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

  3. 12B.2
    The Asymptotic Soliton and Three-Dimensional ShrinkersBook 12B · κ-Solutions and Surgery

    Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.