By Vladimir Rovenski, Pawel Walczak

This quantity has been divided into elements: Geometry and functions. The geometry component of the publication relates basically to geometric flows, laminations, vital formulae, geometry of vector fields on Lie teams and osculation; the articles within the purposes component predicament a few specific difficulties of the idea of dynamical structures, together with mathematical difficulties of liquid flows and a research of cycles for non-dynamical systems.

This paintings is predicated at the moment overseas workshop entitled "Geometry and Symbolic Computations," hung on may possibly 15-18, 2013 on the college of Haifa and is devoted to modeling (using symbolic calculations) in differential geometry and its functions in fields akin to desktop technology, tomography and mechanics. it truly is meant to create a discussion board for college students and researchers in natural and utilized geometry to advertise dialogue of recent state of the art in geometric modeling utilizing symbolic courses akin to Maple™ and Mathematica® , in addition to presentation of latest results.

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17, P. 665–681. 7. Buzano M. Ricci flow on homogeneous spaces with two isotropy summands // Ann. Glob. Anal. Geom. (2014), V. 45, No. 1, P. 25–45. 8. , Knopf D. The Ricci Flow: an Introduction. Mathematical Surveys and Monographs, AMS, Providence, RI, 2004. 9. D’Atri J. , Nickerson N. Geodesic symmetries in space with special curvature tensors // J. Different. Geom. (1974), V. 9, P. 251–262. 10. D’Atri J. , Ziller W. Naturally reductive metrics and Einstein metrics on compact Lie groups // Mem.

Remark 10. x y/=2 C x20 : Remark 11. For k < 0, we will assume (without loss of generality) that e2 D p2;0 ; e3 D p1;1 2 p3;0 ; : : : : for both cases (26) and (27). Indeed, we may use the transformation t 7! x; y/, with k > 0. Remark 12. To determine the first nonzero coefficient em , m 2, it is sufficient to know only pi;j and qi;j , where 2 Ä i C j Ä m. Therefore, we do not need the terms of order i C j > m in calculations using the power series of X and Y . Note also that we do not need the value of k if p2;0 ¤ 0.

Contraction of convex hypersurfaces in Riemannian spaces. J. Diff. Geom. v. 39 (1994) 407–431. 2. , and Baker C. Mean curvature flow of pinched submanifolds to spheres. J. Diff. Geom. v. 85 (2010) 357–395. 3. Baker C. The mean curvature flow of submanifolds of high codimension, 113 pp. 4409 v1. 4. , and Miquel v. Gaussian mean curvature flow. J. of Evolution Equations, v. 10 (2010) 413–423. 5. Brakke K. The motion of a surface by its mean curvature. Prinston, New Jersey: Prinston University Press, 1978.