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We extend a construction by K. Yamato [Ya] to obtain new explicit examples of Riemannian 3-manifolds as in the title. Some of these examples have an interesting geometrical interpretation.

Non-hyperbolic closed geodesics.

Gudlaugur Thorbergsson (1979)

Mathematica Scandinavica

Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres

Karsten Grove, Luigi Verdiani, Burkhard Wilking, Wolfgang Ziller (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In contrast to the homogeneous case, we show that there are compact cohomogeneity one manifolds that do not support invariant metrics of non-negative sectional curvature. In fact we exhibit infinite families of such manifolds including the exotic Kervaire spheres. Such examples exist for any codimension of the singular orbits except for the case when both are equal to two, where existence of non-negatively curved metrics is known.

Non-split almost complex and non-split Riemannian supermanifolds

Matthias Kalus (2019)

Archivum Mathematicum

Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. For almost complex structures, the existence of a splitting is equivalent to the existence of local coordinates in which the almost complex structure can be represented by a purely numerical matrix, i.e. containing no Grassmann variables. For Riemannian metrics, terms up to degree 2 are allowed in...

Nonuniqueness for the heat flow of harmonic maps

J.-M. Coron (1990)

Annales de l'I.H.P. Analyse non linéaire

Note on an inequality

Yongzhong Xu (2006)

Annales de l'I.H.P. Analyse non linéaire

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