Skip to main content
SpringerLink
Log in

Extending Translating Solitons in Semi-Riemannian Manifolds

  • Conference paper
  • First Online:
Lorentzian Geometry and Related Topics (GELOMA 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 211))

Included in the following conference series:

Abstract

In this paper, we recall some general properties and theorems about Translating Solitons in Semi Riemannian Manifolds. Moreover, we investigate those which are invariant by the action of a Lie group of isometries of the ambient space, by paying attention to the behavior close to the singular orbit (if any) and at infinity. Then, we provide some related examples.

Dedicated to Prof. Ceferino Ruiz on his retirement.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. A.V. Alekseevsky, D.V. Alekseevsky, Riemannian \(G\)-Manifold with one-dimensional orbit space. Ann. Global Anal. Geom. 11(3), 197–211 (1993)

    Google Scholar 

  2. J. Clutterbuck, O.C. Schnürer, F. Schulze, Stability of translating solutions to mean curvature flow. Cal. Var. Partial Diff. Eq. 29(3), 281–293 (2007)

    Google Scholar 

  3. E.A. Coddington, N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill Book Company Inc., New York, Toronto, London, 1955)

    MATH  Google Scholar 

  4. M.A. Lawn, M. Ortega, Translating Solitons from Semi-Riemannian foliations (2016). (preprint)

    Google Scholar 

  5. G. Li, D. Tian, C. Wu, Translating solitons of mean curvature flow of noncompact submanifolds. Math. Phys. Anal. Geom. 14, 83–99 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. F. Martin, A. Savas-Halilaj, K. Smoczyk, On the topology of translating solitons of the mean curvature flow, Cal. Var. Partial Diff. Eq. 54(3), 2853–2882 (2015)

    Google Scholar 

  7. X.H. Nguyen, Doubly periodic self-translating surfaces for the mean curvature flow. Geom. Dedicata 174, 177–185 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. B. O’Neill, Semi Riemannian geometry, With applications to relativity, Pure and Applied Mathematics, 103 (Academic Press, Inc., New York, 1983)

    Google Scholar 

  9. S. Wiggins, Introduction to applied nonlinear dynamical systems and chaos. 2nd edn. Texts in Applied Mathematics, 2. Springer-Verlag, New York (2003). ISBN: 0-387-00177-8

    Google Scholar 

Download references

Acknowledgements

M. Ortega has been partially financed by the Spanish Ministry of Economy and Competitiveness and European Regional Development Fund (ERDF), project MTM2016-78807-C2-1-P.

Author information

Authors and Affiliations

  1. Faculty of Science, Department of Mathematics, University of Ankara Tandogan, Ankara, Turkey

    Erdem Kocakuşaklı

  2. Institute of Mathematics Department of Geometry and Topology, University of Granada, Granada, Spain

    Miguel Ortega

Authors
  1. Erdem Kocakuşaklı
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miguel Ortega
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Erdem Kocakuşaklı .

Editor information

Editors and Affiliations

  1. Department of Algebra, Geometry, Topology, University of Malaga, Málaga, Spain

    María A. Cañadas-Pinedo

  2. Department of Algebra, Geometry, Topology, University of Malaga, Málaga, Spain

    José Luis Flores

  3. Department of Applied Mathematics, University of Malaga, Malaga, Spain

    Francisco J. Palomo

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kocakuşaklı, E., Ortega, M. (2017). Extending Translating Solitons in Semi-Riemannian Manifolds. In: Cañadas-Pinedo, M., Flores, J., Palomo, F. (eds) Lorentzian Geometry and Related Topics. GELOMA 2016. Springer Proceedings in Mathematics & Statistics, vol 211. Springer, Cham. https://doi.org/10.1007/978-3-319-66290-9_9

Download citation

Publish with us

Policies and ethics

Search

Navigation