WebDec 1, 2024 · Space forms. Closed hypersurfaces. 1. Introduction. The theory of biharmonic maps plays a fundamental role in many branches of Partial Differential Equations and Differential Geometry. The notion of biharmonic maps, as a natural generalization of harmonic maps, was introduced in 1964 by Eells and Sampson [6], and the related … WebTriharmonic Riemannian submersions from 3-dimensional space forms. Tomoya Miura and Shun Maeta. 5 February 2024 Advances in Geometry, Vol. 21, No. 2. ... Biharmonic hypersurfaces with three distinct principal curvatures in Euclidean 5-space. Yu Fu. 1 Jan 2014 Journal of Geometry and Physics, Vol. 75.
Triharmonic CMC hypersurfaces in space forms with at most 3 distinct ...
WebA triharmonic hypersurfaces in Nn+1(c) is called proper if it is not minimal. In the following, we will consider a CMC proper hypersurface Mn in a space form Nn+1(c). Then (2.6) … WebIn geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface.A hypersurface is a manifold or an algebraic variety of dimension n − 1, which … hunarbaaz winner akash
Triharmonic CMC hypersurfaces in \({\mathbb {R}}^{5}(c)\)
WebJan 1, 2015 · In this paper we shall consider polyharmonic hypersurfaces of order r (briefly, r-harmonic hypersurfaces), where r ≥ 3 is an integer, into a space form Nm+1 (c) of curvature c. WebA hypersurface is said to be totally biharmonic if all its geodesics are biharmonic curves in the ambient space. We prove that a totally biharmonic hypersurface into a space form is … WebAbstract : This article is concerned with the stability of triharmonic maps and in particular triharmonic hypersurfaces. After deriving a number of general statements on the stability of ... hunarmandlar