This thesis studies symmetric spaces G/H with G a semisimple Lie group and where the isotropy subgroup H has a non-discrete center; we will consider the cases when G/H is either a Hermitian, pseudohermitian, or parahermitian symmetric space. For non-compact G with has finite center and H=K is a maximal compact subgroup, G/K is a Hermitian symmetric space of the non-compact type and the Harish-Chandra embedding realizes G/K as a bounded symmetric domain D. Clerc and Ørsted expressed the symplectic area of a geodesic triangle in terms of the Bergman kernel kD of D. We prove a similar formula for the compact dual U/K using a slightly different kernel kc. We give a geometric characterization of the zeroes of this kernel.
Semisimple parahermitian symmetric spaces are also studied using a generalized Borel embedding due to Kaneyuki. We introduce a suitable kernel function and relate it to the symplectic area of geodesic triangles. We also treat complex parahermitian symmetric spaces GC/HC separately. Here GC and HC are complex Lie groups with GC simple. In this case, we introduce a holomorphic kernel function kC and calculate the (complex) symplectic area of geodesic triangles. Finally we show how the other kernels kD and kc may be recovered from the complex kernel kC as suitable restrictions.