Einstein-Weyl deformations and submanifolds

TY - JOUR

T1 - Einstein-Weyl deformations and submanifolds

AU - Pedersen, Henrik

AU - Poon, Yat Sun

AU - Swann, Andrew

PY - 1996/10/1

Y1 - 1996/10/1

N2 - Motivated by new explicit positive Ricci curvature metrics on the four-sphere which are also Einstein-Weyl, we show that the dimension of the Einstein-Weyl moduli near certain Einstein metrics is bounded by the rank of the isometry group and that any Weyl manifold can be embedded as a hypersurface with prescribed second fundamental form in some Einstein-Weyl space. Closed four-dimensional Einstein-Weyl manifolds are proved to be absolute minima of the L2-norm of the curvature of Weyl manifolds and a local version of the Lafontaine inequality is obtained. The above metrics on the four-sphere are shown to contain minimal hypersurfaces isometric to S1 × S2 whose second fundamental form has constant length.

AB - Motivated by new explicit positive Ricci curvature metrics on the four-sphere which are also Einstein-Weyl, we show that the dimension of the Einstein-Weyl moduli near certain Einstein metrics is bounded by the rank of the isometry group and that any Weyl manifold can be embedded as a hypersurface with prescribed second fundamental form in some Einstein-Weyl space. Closed four-dimensional Einstein-Weyl manifolds are proved to be absolute minima of the L2-norm of the curvature of Weyl manifolds and a local version of the Lafontaine inequality is obtained. The above metrics on the four-sphere are shown to contain minimal hypersurfaces isometric to S1 × S2 whose second fundamental form has constant length.

UR - http://www.scopus.com/inward/record.url?scp=0030305907&partnerID=8YFLogxK

U2 - 10.1142/S0129167X96000372

DO - 10.1142/S0129167X96000372

M3 - Journal article

AN - SCOPUS:0030305907

SN - 0129-167X

VL - 7

SP - 705

EP - 719

JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 5

ER -