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Displaying 81 –
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We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.
We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler–Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler–Einstein metrics, and are automatically Kähler–Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existence and regularity results for this flow, as well as stability for the flow near Kähler–Einstein metrics...
2000 Mathematics Subject Classification: Primary 53B35, Secondary 53C50.In dimension greater than four, we prove that if a Hermitian
non-Kaehler manifold is of pointwise constant antiholomorphic sectional
curvatures, then it is of constant sectional curvatures.
We study the compact Hermitian spin surfaces with positive conformal scalar curvature on
which the first eigenvalue of the Dolbeault operator of the spin structure is the
smallest possible. We prove that such a surface is either a ruled surface or a Hopf
surface. We give a complete classification of the ruled surfaces with this property. For
the Hopf surfaces we obtain a partial classification and some examples
A family of integrable geodesic flows is obtained. Any such a family corresponds to a pair of geodesically equivalent metrics.
Currently displaying 81 –
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283