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- W1627480556 abstract "We study the totally null surfaces of the neutral Kahler metric on certain 4-manifolds. The tangent spaces of totally null surfaces are either self-dual (α-planes) or anti-self-dual (β-planes) and so we consider α-surfaces and β-surfaces. The metric of the examples we study,which include the spaces of oriented geodesics of 3-manifolds of constant curvature, are anti-self-dual, and so it is well-known that the α-planes are integrable and α-surfaces exist. These are holomorphic Lagrangiansurfaces, which for the geodesic spaces correspond to totally umbilic foliations of the underlying 3-manifold. The β-surfaces are less known and our interest is mainly in their description. In particular, we classify theβ-surfaces of the neutral Kahler metric on TN, the tangent bundle to a Riemannian 2-manifold N. These include the spaces of oriented geodesics in Euclidean and Lorentz 3-space, for which we show that the β-surfacesare affine tangent bundles to curves of constant geodesic curvature on S2 and H2, respectively. In addition, we construct the β-surfaces of the space of oriented geodesics of hyperbolic 3-space." @default.
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- W1627480556 date "2016-01-01" @default.
- W1627480556 modified "2023-09-27" @default.
- W1627480556 title "Totally Null Surfaces in Neutral K¨ahler 4-Manifolds" @default.
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