ﻻ يوجد ملخص باللغة العربية
Among a family of 2-parameter left invariant metrics on Sp(2), we determine which have nonnegative sectional curvatures and which are Einstein. On the quotiente $widetilde{N}^{11}=(Sp(2)times S^4)/S^3$, we construct a homogeneous isoparametric foliation with isoparametric hypersurfaces diffeomorphic to Sp(2). Furthermore, on the quotiente $widetilde{N}^{11}/S^3$, we construct a transnormal system with transnormal hypersurfaces diffeomorphic to the Gromoll-Meyer sphere $Sigma^7$. Moreover, the induced metric on each hypersurface has positive Ricci curvature and quasi-positive sectional curvature simultaneously.
Gromoll and Meyer have represented a certain exotic 7-sphere $Sigma^7$ as a biquotient of the Lie group $G = Sp(2)$. We show for a 2-parameter family of left invariant metrics on $G$ that the induced metric on $Sigma^7$ has strictly positive sectiona
We study the geometry of the tangent bundle equipped with a two-parameter family of Riemannian metrics. After deriving the expression of the Levi-Civita connection, we compute the Riemann curvature tensor and the sectional, Ricci and scalar curvature
We prove that the group $Aut_1(xi)$ of strict contactomorphisms, also known as quantomorphisms, of the standard tight contact structure $xi$ on $S^3$ is the total space of a fiber bundle $S^1 to Aut_1(xi) to SDiff(S^2)$ over the group of area-preserv
We study the geometry of infinitely presented groups satisfying the small cancelation condition C(1/8), and define a standard decomposition (called the criss-cross decomposition) for the elements of such groups. We use it to prove the Rapid Decay pro
We study harmonic sections of a Riemannian vector bundle whose total space is equipped with a 2-parameter family of metrics which includes both the Sasaki and Cheeger-Gromoll metrics. This enables the theory of harmonic unit sections to be extended to bundles with non-zero Euler class.