Paper · Apr 2, 2020

Some Results on Ricci Flow

Nirabhra Basu, Dipankar Debnath

math.DGarXiv:2004.00961
View PDF View HTML arXiv page

As on arXiv

Abstract

In this paper we have introduced the notion of Ricci flow and shown that Ricci soliton which was introduced by Kakimakamis and Panagiotid in 2014, is a self similar soliton of the Ricci flow. We have also find the deformation of geometric curvature tensors under Ricci flow. In the last two section of the paper, we have found the -functional and functional for Ricci flow respectively.

View PDF View HTML arXiv page
Submitted
Apr 2, 2020
Subjects
math.DG
DOI
10.22190/FUMI2005305D

Comments: 8 pages

Ricci flowRicci solitons

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 A steady length function for Ricci flow (Joshua Jordan, 2020)7Jordan 2020 On the rigidity of harmonic-Ricci solitons (Andrea Anselli, 2020)8Anselli 2020 Characteristics of conformal Ricci soliton on warped product spaces (Dipen Ganguly, Nirabhra Basu and Arindam Bhattacharyya, 2021)2Ganguly 2021 A Study On Some Geometric Properties and Physical Applications of A Mixed Quasi-Einstein Spacetime (Kaushik Chattopadhyay, Arindam Bhattacharyya and Dipankar Debnath, 2021)1Chattopadhya 2021 Characteristics of almost conformal Ricci solitons on Sasakian manifold (Dipen Ganguly, Nirabhra Basu and Arindam Bhattacharyya, 2021)6Ganguly 2021 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)3Mondal 2026 K-contact manifolds admitting some geometric solitons with Semi-Symmetric Non-Metric Connection (Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya, 2026)5Mondal 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. A Study On Some Geometric Properties and Physical Applications of A Mixed Quasi-Einstein Spacetime

    Kaushik Chattopadhyay, Arindam Bhattacharyya and Dipankar Debnath

    Topics Ricci solitons · Same author Dipankar Debnath · Shared terms “curvature tensor”

  2. Characteristics of conformal Ricci soliton on warped product spaces

    Dipen Ganguly, Nirabhra Basu and Arindam Bhattacharyya

    Topics Ricci solitons · Same author Nirabhra Basu

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

    Bidhan Mondal, Sibsankar Panda and Nirabhra Basu

    Topics Ricci solitons · Same author Nirabhra Basu

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

    Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya

    Topics Ricci solitons · Same author Nirabhra Basu · Shared terms “curvature tensor”

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

    Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya

    Topics Ricci solitons · Same author Nirabhra Basu

  6. Characteristics of almost conformal Ricci solitons on Sasakian manifold

    Dipen Ganguly, Nirabhra Basu and Arindam Bhattacharyya

    Topics Ricci solitons · Same author Nirabhra Basu

  7. A steady length function for Ricci flow

    Joshua Jordan

    Topics Ricci solitons

  8. On the rigidity of harmonic-Ricci solitons

    Andrea Anselli

    Topics Ricci solitons · Shared terms “curvature tensor”

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 flow Hamilton's Ricci flow evolves a Riemannian metric by minus twice its Ricci curvature. It is a nonlinear heat equation for geometry: it spreads… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) 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)

In the guidebook

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

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

  2. 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.

  3. 5A.5
    Uniformization and the Two-Dimensional Ricci FlowBook 5A · Complex Analysis and Conformal Geometry

    Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.