کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
840821 908492 2012 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Conditional extremals in complete Riemannian manifolds
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Conditional extremals in complete Riemannian manifolds
چکیده انگلیسی

Conditional extremal curves in a complete Riemannian manifold MM are defined as the critical points of the squared L2L2 distance between the tangent vector field of a curve and a so-called prior   vector field. We prove that this L2L2 distance satisfies the Palais–Smale condition on the space of absolutely continuous curves joining two submanifolds of MM, and thus establish the existence of critical points. We also prove a Morse index theorem in the case where the two submanifolds are single points, and use the Morse inequalities to place lower bounds on the number of critical points of each index.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 75, Issue 4, March 2012, Pages 2177–2188
نویسندگان
, ,