Abstract
In this paper, infinitesimal deformations which preserve the area element of a surface in (A-deformations) which also preserve the lengths of lines of curvature are studied. Here A-deformations are considered up to infinitesimal bendings (which constitute the trivial case for the problem posed). Such A-deformations are also called canonical.For regular surfaces of nonzero total curvature (without umbilic points) the problem indicated reduces to a homogeneous second order partial differential equation of elliptic type. In this paper a series of results about the existence and arbitrariness of canonical A-deformations is obtained. The basic results are valid for surfaces in the large.Bibliography: 20 titles.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
