Geodesic Vector Fields on a Riemannian Manifold
A unit geodesic vector field on a Riemannian manifold is a vector field whose integral curves are geodesics, or in other worlds have zero acceleration. A geodesic vector field on a Riemannian manifold is a smooth vector field with acceleration of each of its integral curves is proportional to veloci...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-01-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/8/1/137 |
| id |
doaj-403a58e5b0c746cfa6039797bd2692e0 |
|---|---|
| record_format |
Article |
| spelling |
doaj-403a58e5b0c746cfa6039797bd2692e02020-11-25T01:10:11ZengMDPI AGMathematics2227-73902020-01-018113710.3390/math8010137math8010137Geodesic Vector Fields on a Riemannian ManifoldSharief Deshmukh0Patrik Peska1Nasser Bin Turki2Department of Mathematics, College of science, King Saud University, P.O. Box-2455 Riyadh 11451, Saudi ArabiaDepartment of Algebra and Geometry, Palacky University, 77146 Olomouc, Czech RepublicDepartment of Mathematics, College of science, King Saud University, P.O. Box-2455 Riyadh 11451, Saudi ArabiaA unit geodesic vector field on a Riemannian manifold is a vector field whose integral curves are geodesics, or in other worlds have zero acceleration. A geodesic vector field on a Riemannian manifold is a smooth vector field with acceleration of each of its integral curves is proportional to velocity. In this paper, we show that the presence of a geodesic vector field on a Riemannian manifold influences its geometry. We find characterizations of <i>n</i>-spheres as well as Euclidean spaces using geodesic vector fields.https://www.mdpi.com/2227-7390/8/1/137geodesic vector fieldeikonal equationisometric to sphereisometric to euclidean space |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Sharief Deshmukh Patrik Peska Nasser Bin Turki |
| spellingShingle |
Sharief Deshmukh Patrik Peska Nasser Bin Turki Geodesic Vector Fields on a Riemannian Manifold Mathematics geodesic vector field eikonal equation isometric to sphere isometric to euclidean space |
| author_facet |
Sharief Deshmukh Patrik Peska Nasser Bin Turki |
| author_sort |
Sharief Deshmukh |
| title |
Geodesic Vector Fields on a Riemannian Manifold |
| title_short |
Geodesic Vector Fields on a Riemannian Manifold |
| title_full |
Geodesic Vector Fields on a Riemannian Manifold |
| title_fullStr |
Geodesic Vector Fields on a Riemannian Manifold |
| title_full_unstemmed |
Geodesic Vector Fields on a Riemannian Manifold |
| title_sort |
geodesic vector fields on a riemannian manifold |
| publisher |
MDPI AG |
| series |
Mathematics |
| issn |
2227-7390 |
| publishDate |
2020-01-01 |
| description |
A unit geodesic vector field on a Riemannian manifold is a vector field whose integral curves are geodesics, or in other worlds have zero acceleration. A geodesic vector field on a Riemannian manifold is a smooth vector field with acceleration of each of its integral curves is proportional to velocity. In this paper, we show that the presence of a geodesic vector field on a Riemannian manifold influences its geometry. We find characterizations of <i>n</i>-spheres as well as Euclidean spaces using geodesic vector fields. |
| topic |
geodesic vector field eikonal equation isometric to sphere isometric to euclidean space |
| url |
https://www.mdpi.com/2227-7390/8/1/137 |
| work_keys_str_mv |
AT shariefdeshmukh geodesicvectorfieldsonariemannianmanifold AT patrikpeska geodesicvectorfieldsonariemannianmanifold AT nasserbinturki geodesicvectorfieldsonariemannianmanifold |
| _version_ |
1725176258134802432 |