Page 1 Next

Displaying 1 – 20 of 287

Showing per page

A geometric problem and the Hopf Lemma. I

Yan Yan Li, Louis Nirenberg (2006)

Journal of the European Mathematical Society

A classical result of A. D. Alexandrov states that a connected compact smooth n -dimensional manifold without boundary, embedded in n + 1 , and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of M in a hyperplane X n + 1 = const in case M satisfies: for any two points ( X ' , X n + 1 ) , ( X ' , X ^ n + 1 ) on M , with X n + 1 > X ^ n + 1 , the mean curvature at the first is not greater than that at the second. Symmetry need not always hold, but in this paper, we establish it under some additional condition for n = 1 . Some variations...

A new approach for describing instantaneous line congruence

Rashad A. Abdel-Baky, Ashwaq J. Al-Bokhary (2008)

Archivum Mathematicum

Based on the E. Study’s map, a new approach describing instantaneous line congruence during the motion of the Darboux frame on a regular non-spherical and non-developable surface, whose parametric curves are lines of curvature, is proposed. Afterward, the pitch of general line congruence is developed and used for deriving necessary and sufficient condition for instantaneous line congruence to be normal. In terms of this, the derived line congruences and their differential geometric invariants were...

Currently displaying 1 – 20 of 287

Page 1 Next