Papers by Isabel Salavessa
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Let E be a Euclidean space. Following Palais, we identify each vector subspace F of E with the or... more Let E be a Euclidean space. Following Palais, we identify each vector subspace F of E with the orthogonal projection πF : E → F . In this way, the Grassman manifold G(E) of all vector subspaces of E appears as a submanifold of the Euclidean space L(E;E) of all linear maps from E into E (with the Hilbert-Schmidt inner product). The aim of this paper is to present some explicit formulas concerning the differential geometry of G(E) as a submanifold of L(E;E). Most of these formulas extend naturally to the case where E is an infinite dimensional Hilbert space, although in this case there is no natural inner product in L(E;E).
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Annals of Global Analysis and Geometry, 2017
Bookmarks Related papers MentionsView impact
Journal of Mathematical Analysis and Applications, 2017
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Manuscr Math, 1993
Bookmarks Related papers MentionsView impact
Portugaliae Mathematica, 2003
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
We define broadly-pluriminimal immersed 2n-submanifold F: M --> N into a Kaehler-Einstein mani... more We define broadly-pluriminimal immersed 2n-submanifold F: M --> N into a Kaehler-Einstein manifold of complex dimension 2n and scalar curvature R. We prove that, if M is compact, n \geq 2, and R < 0, then: (i) Either F has complex or Lagrangian directions; (ii) If n = 2, M is oriented, and F has no complex directions, then it is a Lagrangian submanifold, generalising the well-known case n = 1 for minimal surfaces due to Wolfson. We also prove that, if F has constant Kaehler angles with no complex directions, and is not Lagrangian, then R = 0 must hold. Our main tool is a formula on the Laplacian of a symmetric function on the Kaehler angles.
Bookmarks Related papers MentionsView impact
Proceedings of the American Mathematical Society, 1989
Bookmarks Related papers MentionsView impact
Manuscripta Mathematica, 2012
Bookmarks Related papers MentionsView impact
We prove the mean curvature flow of a spacelike graph in (Σ1×Σ2,g1−g2) of a map f : Σ1 → Σ2 from ... more We prove the mean curvature flow of a spacelike graph in (Σ1×Σ2,g1−g2) of a map f : Σ1 → Σ2 from a closed Riemannian manifold (Σ1,g1) with Ricci1 > 0 to a complete Riemannian manifold (Σ2,g2) with bounded curvature tensor and derivatives, and with K2 ≤ K1, remains a spacelike graph, exists for all time, and converges to a slice at infinity. We al so show, with no need of the assumption K2 ≤ K1, that if K1 > 0, or if Ricci1 > 0 and K2 ≤ −c, c > 0 constant, any mapf : Σ1 → Σ2 is trivially homotopic provided f ∗g2 < ρg1 whereρ = minΣ1 K1/supΣ2 K + 2 ≥ 0. This largely extends some known results for Ki constant andρ = 1.
Bookmarks Related papers MentionsView impact
Pac J Math, 2002
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Monatshefte für Mathematik, 2009
Bookmarks Related papers MentionsView impact
Monatshefte für Mathematik, 2010
Bookmarks Related papers MentionsView impact
Calculus of Variations and Partial Differential Equations, 2013
ABSTRACT
Bookmarks Related papers MentionsView impact
Uploads
Papers by Isabel Salavessa