Harmonic-hyperbolic geometric flow
In this article we study a coupled system for hyperbolic geometric flow on a closed manifold M, with a harmonic flow map from M to some closed target manifold N. Then we show that this flow has a unique solution for a short-time. After that, we find evolution equations for Riemannian curvature...
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| Language: | English |
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Texas State University
2017-07-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/165/abstr.html |
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doaj-8bf5b6765f7242059f2361115b0ed8432020-11-24T22:33:41ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912017-07-012017165,19Harmonic-hyperbolic geometric flowShahroud Azami0 Imam Khomeini International Univ., Qazvin, Iran In this article we study a coupled system for hyperbolic geometric flow on a closed manifold M, with a harmonic flow map from M to some closed target manifold N. Then we show that this flow has a unique solution for a short-time. After that, we find evolution equations for Riemannian curvature tensor, Ricci curvature tensor, and scalar curvature of M under this flow. In the final section we give some examples of this flow on closed manifolds.http://ejde.math.txstate.edu/Volumes/2017/165/abstr.htmlHyperbolic geometric flowquasilinear hyperbolic equationstrict hyperbolicity |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Shahroud Azami |
| spellingShingle |
Shahroud Azami Harmonic-hyperbolic geometric flow Electronic Journal of Differential Equations Hyperbolic geometric flow quasilinear hyperbolic equation strict hyperbolicity |
| author_facet |
Shahroud Azami |
| author_sort |
Shahroud Azami |
| title |
Harmonic-hyperbolic geometric flow |
| title_short |
Harmonic-hyperbolic geometric flow |
| title_full |
Harmonic-hyperbolic geometric flow |
| title_fullStr |
Harmonic-hyperbolic geometric flow |
| title_full_unstemmed |
Harmonic-hyperbolic geometric flow |
| title_sort |
harmonic-hyperbolic geometric flow |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2017-07-01 |
| description |
In this article we study a coupled system for hyperbolic geometric
flow on a closed manifold M, with a harmonic flow map from M to
some closed target manifold N.
Then we show that this flow has a unique solution for a short-time.
After that, we find evolution equations for Riemannian curvature tensor,
Ricci curvature tensor, and scalar curvature of M under this flow.
In the final section we give some examples of this flow on closed manifolds. |
| topic |
Hyperbolic geometric flow quasilinear hyperbolic equation strict hyperbolicity |
| url |
http://ejde.math.txstate.edu/Volumes/2017/165/abstr.html |
| work_keys_str_mv |
AT shahroudazami harmonichyperbolicgeometricflow |
| _version_ |
1725729879583883264 |