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Systoles of Surfaces
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, systolic inequalities for curves on surfaces were first studied by Charles Loewner in 1949 (unpublished; see remark at end of Pu''s paper in ''52). Given a closed surface, its systole, denoted sys, is defined to the least length of a loop that cannot be contracted to a point on the surface. The systolic area of a metric is defined to be the ratio area/sys2. The systolic ratio SR is the reciprocal quantity sys2/area. See also Introduction to systolic geometry. A similar result is given by Pu''s inequality for the real projective plane from 1952, due to Pao Ming Pu, with an upper bound of /2 for the systolic ratio SR(RP2), also attained in the constant curvature case.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131242946
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Größe H220mm x B220mm
- EAN 9786131242946
- Format Fachbuch
- Titel Systoles of Surfaces
- Herausgeber Betascript Publishing
- Anzahl Seiten 108
- Genre Mathematik
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