cover image: Calcutta University Readership Lectures  1930. Selected Problems of Differential Geometry

Premium

20.500.12592/q61jdh

Calcutta University Readership Lectures 1930. Selected Problems of Differential Geometry

1934

The sum of lengths of the arcs of C contained in this stripe has to be equal to the sum of lengths of the two arcs in the stripe and on C. The general convex surfaces having our property are not very well-known. [...] In calculus of variations one considers con- jugate points on a geodetic G. If p is a point of G. we consider all geodetics through p and the next point p on G, where G touches the envelope of the geodetics through p. This is the next conjugate point p of p on G. The sphere has the property that p and p are opposite points, which means the conjugate point of p is independent of the choice of the [...] the upper limit o of the area of a triangle with the corners in the convex point set C. Between t:1 and the area a of any convex point-set C we have the inequality a The equality holds if and only if the boundary of C is an ellipse. [...] In the special case of a web contain- ing 2 sheaves of parallel straight lines this sheaf of surfaces is the sheaf of parallel planes parallel to the 2 directions of the straight lines. [...] I shall give you a sketch of a result contained in a paper of Graf and Satter in 1924. 15 The theorem is the following : The most general straight lined hexagonal 3-web is formed by the tangents of a curve of third class.
technology medicine science
Pages
40
Published in
India
SARF Document ID
sarf.100014
Segment Pages Author Actions
Frontmatter
i-iv W. Blaschke view
Introduction
1-1 unknown view
Lecture I Three Examples of Integral Geometry
2-7 unknown view
Lecture II On Affine Geometry
8-15 unknown view
Lectures III IV V & VI On Topological Geometry
16-36 unknown view

Related Topics

All