ترغب بنشر مسار تعليمي؟ اضغط هنا

On Rank Problems for Planar Webs and Projective Structures

126   0   0.0 ( 0 )
 نشر من قبل Vladislav V. Goldberg
 تاريخ النشر 2008
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We present old and recent results on rank problems and linearizability of geodesic planar webs.


قيم البحث

اقرأ أيضاً

We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads to the direct web-theoretical proo f of the Poincar{e}s theorem: a planar 4-web of maximum rank is linearizable. We also find an invariant intrinsic characterization of planar 4-webs of rank two and one and prove that in general such webs are not linearizable. This solves the Blaschke problem ``to find invariant conditions for a planar 4-web to be of rank 1 or 2 or 3. Finally, we find invariant characterization of planar 5-webs of maximum rank and prove than in general such webs are not linearizable.
We present a complete description of a class of linearizable planar geodesic webs which contain a parallelizable 3-subweb.
The authors found necessary and sufficient conditions for Samuelsons web to be of maximum rank.
484 - Olivier Guichard 2007
In this article we give a geometric interpretation of the Hitchin component for PSL(4,R) in the representation variety of a closed oriented surface of higher genus. We show that representations in the Hitchin component are precisely the holonomy repr esentations of properly convex foliated projective structures on the unit tangent bundle of the surface. From this we also deduce a geometric description of the Hitchin component the symplectic group PSp(4,R).
We establish an explicit correspondence between two--dimensional projective structures admitting a projective vector field, and a class of solutions to the $SU(infty)$ Toda equation. We give several examples of new, explicit solutions of the Toda equ ation, and construct their mini--twistor spaces. Finally we discuss the projective-to-Einstein correspondence, which gives a neutral signature Einstein metric on a cotangent bundle $T^*N$ of any projective structure $(N, [ abla])$. We show that there is a canonical Einstein of metric on an $R^*$--bundle over $T^*N$, with a connection whose curvature is the pull--back of the natural symplectic structure from $T^*N$.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا