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On Gaussian and Geodesic Curvature of Riemannian Manifolds
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| Zeitschriftentitel: | Canadian Journal of Mathematics |
|---|---|
| Personen und Körperschaften: | |
| In: | Canadian Journal of Mathematics, 26, 1974, 3, S. 629-635 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Canadian Mathematical Society
|
| Schlagwörter: |
| author_facet |
Rummler, Hansklaus Rummler, Hansklaus |
|---|---|
| author |
Rummler, Hansklaus |
| spellingShingle |
Rummler, Hansklaus Canadian Journal of Mathematics On Gaussian and Geodesic Curvature of Riemannian Manifolds General Mathematics |
| author_sort |
rummler, hansklaus |
| spelling |
Rummler, Hansklaus 0008-414X 1496-4279 Canadian Mathematical Society General Mathematics http://dx.doi.org/10.4153/cjm-1974-060-x <jats:p>In [1], S. S. Chern gave a very elegant and simple proof of the Gauss-Bonnet formula for closed (i.e. compact without boundary) oriented Riemannian manifolds of even dimension:</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" orientation="portrait" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S0008414X00049142_eqn01" /></jats:disp-formula></jats:p><jats:p>Here, <jats:italic>c</jats:italic> is a suitable constant depending on the dimension of <jats:italic>M</jats:italic> and <jats:italic>Ω</jats:italic> is an <jats:italic>n</jats:italic>-form (<jats:italic>n</jats:italic> = dim <jats:italic>M</jats:italic>) which may be calculated from its curvature tensor. W. Greub gave a coordinate-free description of this integrand <jats:italic>Ω</jats:italic> (cf. [4]).</jats:p> On Gaussian and Geodesic Curvature of Riemannian Manifolds Canadian Journal of Mathematics |
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Canadian Mathematical Society, 1974 |
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Canadian Mathematical Society, 1974 |
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0008-414X 1496-4279 |
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1974 |
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Canadian Mathematical Society |
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Canadian Journal of Mathematics |
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| title |
On Gaussian and Geodesic Curvature of Riemannian Manifolds |
| title_unstemmed |
On Gaussian and Geodesic Curvature of Riemannian Manifolds |
| title_full |
On Gaussian and Geodesic Curvature of Riemannian Manifolds |
| title_fullStr |
On Gaussian and Geodesic Curvature of Riemannian Manifolds |
| title_full_unstemmed |
On Gaussian and Geodesic Curvature of Riemannian Manifolds |
| title_short |
On Gaussian and Geodesic Curvature of Riemannian Manifolds |
| title_sort |
on gaussian and geodesic curvature of riemannian manifolds |
| topic |
General Mathematics |
| url |
http://dx.doi.org/10.4153/cjm-1974-060-x |
| publishDate |
1974 |
| physical |
629-635 |
| description |
<jats:p>In [1], S. S. Chern gave a very elegant and simple proof of the Gauss-Bonnet formula for closed (i.e. compact without boundary) oriented Riemannian manifolds of even dimension:</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" orientation="portrait" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S0008414X00049142_eqn01" /></jats:disp-formula></jats:p><jats:p>Here, <jats:italic>c</jats:italic> is a suitable constant depending on the dimension of <jats:italic>M</jats:italic> and <jats:italic>Ω</jats:italic> is an <jats:italic>n</jats:italic>-form (<jats:italic>n</jats:italic> = dim <jats:italic>M</jats:italic>) which may be calculated from its curvature tensor. W. Greub gave a coordinate-free description of this integrand <jats:italic>Ω</jats:italic> (cf. [4]).</jats:p> |
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| description | <jats:p>In [1], S. S. Chern gave a very elegant and simple proof of the Gauss-Bonnet formula for closed (i.e. compact without boundary) oriented Riemannian manifolds of even dimension:</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" orientation="portrait" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S0008414X00049142_eqn01" /></jats:disp-formula></jats:p><jats:p>Here, <jats:italic>c</jats:italic> is a suitable constant depending on the dimension of <jats:italic>M</jats:italic> and <jats:italic>Ω</jats:italic> is an <jats:italic>n</jats:italic>-form (<jats:italic>n</jats:italic> = dim <jats:italic>M</jats:italic>) which may be calculated from its curvature tensor. W. Greub gave a coordinate-free description of this integrand <jats:italic>Ω</jats:italic> (cf. [4]).</jats:p> |
| doi_str_mv | 10.4153/cjm-1974-060-x |
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| imprint | Canadian Mathematical Society, 1974 |
| imprint_str_mv | Canadian Mathematical Society, 1974 |
| institution | DE-D275, DE-Bn3, DE-Brt1, DE-Zwi2, DE-D161, DE-Gla1, DE-Zi4, DE-15, DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229 |
| issn | 0008-414X, 1496-4279 |
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| language | English |
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| physical | 629-635 |
| publishDate | 1974 |
| publishDateSort | 1974 |
| publisher | Canadian Mathematical Society |
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| series | Canadian Journal of Mathematics |
| source_id | 49 |
| spelling | Rummler, Hansklaus 0008-414X 1496-4279 Canadian Mathematical Society General Mathematics http://dx.doi.org/10.4153/cjm-1974-060-x <jats:p>In [1], S. S. Chern gave a very elegant and simple proof of the Gauss-Bonnet formula for closed (i.e. compact without boundary) oriented Riemannian manifolds of even dimension:</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" orientation="portrait" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S0008414X00049142_eqn01" /></jats:disp-formula></jats:p><jats:p>Here, <jats:italic>c</jats:italic> is a suitable constant depending on the dimension of <jats:italic>M</jats:italic> and <jats:italic>Ω</jats:italic> is an <jats:italic>n</jats:italic>-form (<jats:italic>n</jats:italic> = dim <jats:italic>M</jats:italic>) which may be calculated from its curvature tensor. W. Greub gave a coordinate-free description of this integrand <jats:italic>Ω</jats:italic> (cf. [4]).</jats:p> On Gaussian and Geodesic Curvature of Riemannian Manifolds Canadian Journal of Mathematics |
| spellingShingle | Rummler, Hansklaus, Canadian Journal of Mathematics, On Gaussian and Geodesic Curvature of Riemannian Manifolds, General Mathematics |
| title | On Gaussian and Geodesic Curvature of Riemannian Manifolds |
| title_full | On Gaussian and Geodesic Curvature of Riemannian Manifolds |
| title_fullStr | On Gaussian and Geodesic Curvature of Riemannian Manifolds |
| title_full_unstemmed | On Gaussian and Geodesic Curvature of Riemannian Manifolds |
| title_short | On Gaussian and Geodesic Curvature of Riemannian Manifolds |
| title_sort | on gaussian and geodesic curvature of riemannian manifolds |
| title_unstemmed | On Gaussian and Geodesic Curvature of Riemannian Manifolds |
| topic | General Mathematics |
| url | http://dx.doi.org/10.4153/cjm-1974-060-x |