Let M be the moduli space of irreducible flat PSL(2,R) connections on a punctured surface of finite type with parabolic holonomies around punctures. By using a notion of admissibility of an ideal arc, M is covered by dense open subsets associated to ideal triangulations of the surface. A principal bundle over M is cons…
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7 results for “S-coordinates”
Revisited study of real Jacobi group with invariant metrics and forms.
problem Characterizing the real Jacobi group and its invariant structures.
method Matrix realization, S-coordinates, left-invariant forms and metrics.
result Invariant metrics and forms on the Jacobi group and its quotients.
We construct a geometric, real analytic parametrization of the Hitchin component Hit_n(S) of the PSL_n(R)-character variety R_{PSL_n(R)}(S) of a closed surface S. The approach is explicit and constructive. In essence, our parametrization is an extension of Thurston's shear coordinates for the Teichmueller space of a cl…
Geodesics on extended Siegel-Jacobi upper half-plane determined.
problem Determining geodesics on a complex geometric space.
method Equating parameters in geodesic equations on the extended Siegel-Jacobi upper half-plane.
result Geodesic equations on Siegel-Jacobi, Siegel, and Heisenberg spaces.
Extended Siegel-Jacobi upper half-plane geometry studied with invariant metrics.
problem Characterizing the geometry of the extended Siegel-Jacobi upper half-plane.
method Parameterized using S-coordinates and expressed in terms of invariant metrics.
result Extended Siegel-Jacobi upper half-plane is a reductive, non-symmetric manifold.
Extended metric defined on Siegel-Jacobi space using invariant forms.
problem Defining a metric on the extended Siegel-Jacobi upper half space.
method Matrix embedding, pre-Iwasawa decomposition, invariant forms, sum of squares of forms.
result Invariant metric on the extended Siegel-Jacobi upper half space is derived.
Improves disease progression prediction using auxiliary surrogate labels and health markers.
problem Challenges in predicting disease progression due to unknown true disease states.
method Integrates hidden Markov model with time-varying discriminative classification model.
result Significant improvement in distinguishing LBD from AD using objective markers.