Paper · Apr 15, 2018

Remarks on almost -Ricci solitons in -para Sasakian manifolds

Adara M. Blaga, Selcen Yuksel Perktas

math.DGarXiv:1804.05389
View PDF View HTML arXiv page

As on arXiv

Abstract

We consider almost -Ricci solitons in -para Sasakian manifolds satisfying certain curvature conditions. In the gradient case we give an estimation of the Ricci curvature tensor's norm and express the scalar curvature of the manifold in terms of the functions that define the soliton. We also prove that if the Ricci operator is Codazzi, then the gradient -Ricci soliton is expanding if is spacelike or shrinking if is timelike.

View PDF View HTML arXiv page
Submitted
Apr 15, 2018
Subjects
math.DG
Journal
Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68(2), 1621-1628 (2019)
DOI
10.31801/cfsuasmas.546595

Comments: 9 pages

Ricci solitonsAlmost & η-Ricci solitonsScalar curvatureSasakian & contact geometryPhysics

Its neighbourhood

Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2016, plus the canon.

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 η-Ricci solitons in (ε)-almost paracontact metric manifolds (Adara Monica Blaga, Selcen Yüksel Perktaş, Bilal Eftal Acet et al., 2017)2Blaga 2017 Almost η-Ricci solitons in (LCS)ₙ-manifolds (Adara M. Blaga, 2017)7Blaga 2017 Para-Sasakian manifolds and *-Ricci solitons (D. G. Prakasha and Pundikala Veeresha, 2018)1Prakasha 2018 Sasakian Manifold and *-Ricci Tensor (Venkatesha. and Aruna Kumara H, 2018)6Venkatesha. 2018 *-Conformal η-Ricci Soliton on Sasakian manifold (Soumendu Roy, Santu Dey, Arindam Bhattacharyya et al., 2019)4Roy 2019 Geometric solitons in a D-homothetically deformed Kenmotsu manifold (Adara M. Blaga, 2020)8Blaga 2020 Remarks on Riemann and Ricci solitons in (α,β)-contact metric manifolds (Adara M. Blaga and Dan Radu Latcu, 2020)5Blaga 2020 Geometry of para-Sasakian metric as an almost conformal η-Ricci soliton (Sumanjit Sarkar, Santu Dey and Arindam Bhattacharyya, 2021)3Sarkar 2021
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Para-Sasakian manifolds and *-Ricci solitons

    D. G. Prakasha and Pundikala Veeresha

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “para Sasakian”

  2. -Ricci solitons in -almost paracontact metric manifolds

    Adara Monica Blaga, Selcen Yüksel Perktaş, Bilal Eftal Acet et al.

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same authors Adara M. Blaga, Selcen Yuksel Perktas · Shared terms “para Sasakian”

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

    Sumanjit Sarkar, Santu Dey and Arindam Bhattacharyya

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Scalar curvature · Shared terms “para Sasakian”

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

    Soumendu Roy, Santu Dey, Arindam Bhattacharyya et al.

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “manifolds satisfying”, “curvature tensor”

  5. Remarks on Riemann and Ricci solitons in -contact metric manifolds

    Adara M. Blaga and Dan Radu Latcu

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “manifolds satisfying”

  6. Sasakian Manifold and *-Ricci Tensor

    Venkatesha. and Aruna Kumara H

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons

  7. Almost -Ricci solitons in -manifolds

    Adara M. Blaga

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “manifolds satisfying”, “curvature condition”

  8. Geometric solitons in a -homothetically deformed Kenmotsu manifold

    Adara M. Blaga

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Scalar curvature · Same author Adara M. Blaga

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) 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.