Abstract: This Lecture presents the geometry and the interaction of nonholonomic black hole systems using a specialized MAPLE soft for computing. Our point of view is strongly connected to the possibility of describing a nonholonomic black hole system via a Gibbs-Pfaff equation, or to the possibility of having extremum problems with nonholonomic constraints.
Section 1 introduces a nonholonomic black hole system and proves that the existence of an integral surface of the Gibbs-Pfaff equation implies the second area condition (the equality of two elements of area). Section 2 shows that the equilibrium after interaction of two nonholonomic black hole systems is realized at equal temperatures and equal angular velocities. Section 3 uses the nonholonomic theory of Vranceanu to build the subriemannian geometry of black holes. Section 4 computes the coefficients of the bilinear covariants of the Gibbs-Vranceanu co-framed nonholonomic space. The geometry of the Gibbs-Vranceanu-Riemann nonholonomic space is represented by the Ricci rotation coefficients (Section 5), the geodesics (Section 6), the Ricci coefficients with four indexes (Section 7), the Ricci tensor and the scalar curvature (Section 8). We introduce also some interesting submanifolds: the submanifold of the coefficients of bilinear covariants (Section 9), the submanifold of Ricci rotation coefficients (Section 10), the submanifold of Ricci coefficients with four indexes (Section 11). Section 12 underlines that some properties of black holes can be obtained using geometric tools in MAPLE version.

Brief Biography of the Speaker:
Important Career Positions: Dean, Director, Chair, Full Professor 1990-, University Politehnica of Bucharest, Department of Mathematics-Informatics I.
Number of PhD Students: 25 in due time and 14 Doctors in Mathematics.
Membership of Associations: AMS, 1987; Tensor Society, 1985; Balkan Society of Geometers, President, 1994;
Publications: over 40 books; 230 papers; 230 communications.
Honours: D. Hurmuzescu Prize, Romanian Academy, 1985; Award MEI, 1988; Correspondent Member, Academia Peloritana, Messina, 1997; Titular Member, Academy of Romanian Scientists, 2007; Honorary Member, World Scientific and Engineering Academy and Society, 2008-;
Main Organizer: The International Conference of Differential Geometry and Dynamical Systems, University Politehnica of Bucharest, October 5-7, 2007; The International Conference of Differential Geometry and Dynamical Systems, The V-th International Colloquium of Mathematics in Engineering and Numerical Physics, August 29-September 02, 2008; The International Conference of Differential Geometry and Dynamical Systems, University Politehnica of Bucharest, October 7-11, 2009.
Chair Committee or Member of the International Advisory Committee: 7th WSEAS International Conference on Systems Theory and Scientific Computation (ISTASC-07), Vouliagmeni Beach, Athens, Greece, August 24-26 (2007); European Computing Conference, Vouliagmeni Beach, Athens, Greece, September 24-26, 2007; 12th WSEAS International Conference on Applied Mathematics, Cairo, Egypt, Dec. 29-31, 2007; 7th WSEAS International Conference on Circuits, Systems, Electronics, Control and Signal Processing, Cairo, Egypt, Dec. 29-31, 2007; Chair-Committee: American Conference on Applied Mathematics (Math-08) and Management, Marketing and Finances (MMF-08), Cambridge, Massachusetts, USA, March 24-26, 2008; International Program Committee: The Applied Computing Conference (ACC-08), Istanbul, Turkey, May 27-30, 2008; European Computing Conference (ECC-09), Tbilisi, Georgia, June 26-28, 2009; The 9th WSEAS International Conference on Applied Informatics and Communications (AIC-09), Moscow, Russia, August 20-22, 2009; The 10th International Conference on Applied Computer Science (ACS-10), Iwate, Japan, October 4-6, 2010.
Fields of Interest: Differential Geometry, Optimizations on Riemannian Manifolds, Magnetic Dynamical Systems, Geometric Dynamics, Multitime Optimal Control.