Warped products and Spaces of Constant Curvature

We will obtain the warped product decompositions of spaces of constant curvature (with arbitrary signature) in their natural models as subsets of pseudo-Euclidean space. This generalizes the corresponding result by S. Nolker to arbitrary signatures, and has a similar level of detail. Although our derivation is complete in some sense, none is proven. Motivated by applications, we will give more information for the spaces with Euclidean and Lorentzian signatures. This is an expository article which is intended to be used as a reference. So we also give a review of the theory of circles and spheres in pseudo-Riemannian manifolds

Astrophysical plasmas and fluids

This book is a valuable introduction to astrophyscial plasmas and fluids for graduate students of astronomy preparing either for a research career in the field or just aspiring to achieve a decent degree of familiarity with 99% of the cosmos. The contents provide a true representation of the phenomenal diversity of dominant roles that plasmas and fluids play in the near and far reaches of the universe. The breadth of coverage of basic physical processes is a particularly attractive feature of this text book. By first using the Liouville equation to derive the kinetic, the two-fluid and single-fluid, descriptions of a plasma and a fluid, and then demonstrating the use of these descriptions for specific situations in the rest of the book, the author has probably chosen the most efficient way of handling this large technical subject. The two major astrophysical issues, fluid or plasma configurations and their radiative signatures, figure prominently througout the book. The problems are designed to give the reader a feel for the quantititative properties of celestial objects.Comment: 3 pages tex file

Stimulated Raman scattering of water maser lines in astrophysical plasmas

Radiative transfer equations are derived and solved for the stimulated Raman scattering of water maser lines in the astrophysical plasmas with electron density of about 10^6 - 10^7 cm-3. In stimulated Raman scattering, the energy of water maser line is transferred to the side band modes: Stokes mode and anti-Stokes mode. The Stokes mode is easily produced by backward Raman scattering while the anti-Stokes mode is created by the interacting intersecting masers in the plasma. The intensity of the Stokes mode is higher than that of the anti-Stokes mode. These side band modes are proposed as explanation for the extreme velocity features observed in the galaxy NGC 4258. The threshold value of the brightness temperature for the Raman scattering is about 10^16 - 10^19 K, and it is satisfied in the case of NGC 4258.Comment: 12 pages, 4 Postscript figures. Accepted for Physics of Plasma