منابع مشابه
Timelike Surfaces with Harmonic Inverse Mean Curvature
In classical differential geometry, surfaces of constant mean curvature (CMC surfaces) have been studied extensively [1]. As a generalization of CMC surfaces, Bobenko [2] introduced the notion of surface with harmonic inverse mean curvature (HIMC surface). He showed that HIMC surfaces admit Lax representation with variable spectral parameter. In [5], Bobenko, Eitner and Kitaev showed that the G...
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We study a class of timelike weakly extremal surfaces in flat Minkowski space R, characterized by the fact that they admit a C parametrization (in general not an immersion) of a specific form. We prove that if the distinguished parametrization is of class C, then the surface is regularly immersed away from a closed singular set of euclidean Hausdorff dimension at most 1 + 1/k, and that this bou...
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We construct a canonical formulation of general relativity for the case of a timelike foliation of spacetime. The formulation possesses explicit covariance with respect to Lorentz transformations in the tangent space. Applying the loop approach to quantize the theory we derive the spectrum of the area operator of a two-dimensional surface. Its different branches are naturally associated to spac...
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We discuss the geometry of timelike surfaces (two-dimensional submanifolds) in a Lorentzian manifold and its interpretation in terms of general relativity. A classification of such surfaces is presented which distinguishes four cases of special algebraic properties of the second fundamental form from the generic case. In the physical interpretation a timelike surface Σ can be viewed as the worl...
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ژورنال
عنوان ژورنال: Classical and Quantum Gravity
سال: 2010
ISSN: 0264-9381,1361-6382
DOI: 10.1088/0264-9381/27/15/155014