A note on the Gauss maps of Cayley-free embeddings into spin(7)-manifolds

We show that a closed, orientable 4-manifold M admits a Cayley-free embedding into flat Spin(7)-manifold R-8 if and only if both the Euler characteristic chi(M) and the signature tau(M) of M vanish.


On endomorphisms of surface mapping class groups
Korkmaz, Mustafa (Elsevier BV, 2001-05-01)
In this paper, we prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.
An obstruction to the existence of real projective structures
Coban, Hatice (Elsevier BV, 2019-09-15)
In this short note, we give an obstruction to obtain examples of higher dimensional manifolds with infinite fundamental groups, including the infinite cyclic group Z, admitting no real projective structure.
Affine Osserman connections and their Riemann extensions
Garcia-Rio, E; Kupeli, DN; Vazquez-Abal, ME; Vazquez-Lorenzo, R (Elsevier BV, 1999-09-01)
Osserman property is studied for affine torsion-free connections with special attention to the 2-dimensional case. As an application, examples of nonsymmetric and even not locally homogeneous Osserman pseudo-Riemannian metrics are constructed on the cotangent bundle of a manifold equipped with a torsionfree connection by looking at their Riemann extensions. Also, timelike and spacelike Osserman conditions are analyzed for general pseudo-Riemannian manifolds showing that they are equivalent.
Equivariant cross sections of complex Stiefel manifolds
Onder, T (Elsevier BV, 2001-01-16)
Let G be a finite group and let M be a unitary representation space of G. A solution to the existence problem of G-equivariant cross sections of the complex Stiefel manifold W-k(M) of unitary k-frames over the unit sphere S(M) is given under mild restrictions on G and on fixed point sets. In the case G is an even ordered group, some sufficient conditions for the existence of G-equivariant real frame fields on spheres with complementary G-equivariant complex structures are also obtained, improving earlier re...
A note on b-weakly compact operators
Alpay, Safak; Altin, Birol (Springer Science and Business Media LLC, 2007-11-01)
We consider a continuous operator T : E -> X where E is a Banach lattice and X is a Banach space. We characterize the b-weak compactness of T in terms of its mapping properties.
Citation Formats
İ. Ünal, “A note on the Gauss maps of Cayley-free embeddings into spin(7)-manifolds,” DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, pp. 1–8, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47849.