Almost complex structure and the quotient four-manifold by an anti-symplectic involution

Using the Nambu-Goto string action in the space of the surfaces spanned by closed strings in a spacetime manifold, we investigated the geodesic surface equation in the space of surfaces joining two given strings and the geodesic surface deviation equation in geodesic surface congruence which yields a Jacobi field along a given geodesic surface, and singularities in geodesic surface congruences. In this paper, assuming that the singularity exists in geodesic surface congruences in a conformally symmetric manifold, we compute the Jacobi fields of the geodesic surface deviation equations and observe them.

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Quantum Cohomologies of Symmetric Products

Cho

2012

Int. J. Geom. Methods Mod. Phys.

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In this paper we investigate the quantum cohomologies of symmetric products of Kähler manifolds. To do this we study the moduli space of product space and symmetric group action on it, Gromov-Witten invariant and relative Gromov-Witten invariant. Also we investigate the relations between symmetric invariant properties on the products space and the corresponding ones on the symmetric product. As an example we examine the symmetric product of k copies complex projective line P 1 , which is the k-dimensional complex projective space P k .

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Almost complex structure and the quotient four-manifold by an anti-symplectic involution

Cited by 4 publications

References 19 publications

Finite group action and Gromov-Witten invariants in symplectic four-manifolds

Finite group action and Gromov-Witten invariants in symplectic four-manifolds

Jacobi Fields in Geodesic Surface Congruences

Quantum Cohomologies of Symmetric Products

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