From infinitesimal harmonic transformations to Ricci solitons

Sergey E. Stepanov; Irina I. Tsyganok; Josef Mikeš

Mathematica Bohemica (2013)

  • Volume: 138, Issue: 1, page 25-36
  • ISSN: 0862-7959

Abstract

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The concept of the Ricci soliton was introduced by R. S. Hamilton. The Ricci soliton is defined by a vector field and it is a natural generalization of the Einstein metric. We have shown earlier that the vector field of the Ricci soliton is an infinitesimal harmonic transformation. In our paper, we survey Ricci solitons geometry as an application of the theory of infinitesimal harmonic transformations.

How to cite

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Stepanov, Sergey E., Tsyganok, Irina I., and Mikeš, Josef. "From infinitesimal harmonic transformations to Ricci solitons." Mathematica Bohemica 138.1 (2013): 25-36. <http://eudml.org/doc/252554>.

@article{Stepanov2013,
abstract = {The concept of the Ricci soliton was introduced by R. S. Hamilton. The Ricci soliton is defined by a vector field and it is a natural generalization of the Einstein metric. We have shown earlier that the vector field of the Ricci soliton is an infinitesimal harmonic transformation. In our paper, we survey Ricci solitons geometry as an application of the theory of infinitesimal harmonic transformations.},
author = {Stepanov, Sergey E., Tsyganok, Irina I., Mikeš, Josef},
journal = {Mathematica Bohemica},
keywords = {Ricci soliton; infinitesimal harmonic transformation; Riemannian manifold; Ricci soliton; infinitesimal harmonic transformation; Riemannian manifold},
language = {eng},
number = {1},
pages = {25-36},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {From infinitesimal harmonic transformations to Ricci solitons},
url = {http://eudml.org/doc/252554},
volume = {138},
year = {2013},
}

TY - JOUR
AU - Stepanov, Sergey E.
AU - Tsyganok, Irina I.
AU - Mikeš, Josef
TI - From infinitesimal harmonic transformations to Ricci solitons
JO - Mathematica Bohemica
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 138
IS - 1
SP - 25
EP - 36
AB - The concept of the Ricci soliton was introduced by R. S. Hamilton. The Ricci soliton is defined by a vector field and it is a natural generalization of the Einstein metric. We have shown earlier that the vector field of the Ricci soliton is an infinitesimal harmonic transformation. In our paper, we survey Ricci solitons geometry as an application of the theory of infinitesimal harmonic transformations.
LA - eng
KW - Ricci soliton; infinitesimal harmonic transformation; Riemannian manifold; Ricci soliton; infinitesimal harmonic transformation; Riemannian manifold
UR - http://eudml.org/doc/252554
ER -

References

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