Bi-Legendrian manifolds and paracontact geometry

We study the interplays between paracontact geometry and the theory of bi-Legendrian manifolds. We interpret the bi-Legendrian connection of a bi-Legendrian manifold M as the paracontact connection of a canonical paracontact structure induced on M and then we discuss many consequences of this result both for bi-Legendrian and for paracontact manifolds. Finally new classes of examples of paracontact manifolds are presented.Comment: to appear in Int. J. Geom. Meth. Mod. Phy

A splitting theorem for Kahler manifolds whose Ricci tensors have constant eigenvalues

It is proved that a compact Kahler manifold whose Ricci tensor has two distinct, constant, non-negative eigenvalues is locally the product of two Kahler-Einstein manifolds. A stronger result is established for the case of Kahler surfaces. Irreducible Kahler manifolds with two distinct, constant eigenvalues of the Ricci tensor are shown to exist in various situations: there are homogeneous examples of any complex dimension n > 1, if one eigenvalue is negative and the other positive or zero, and of any complex dimension n > 2, if the both eigenvalues are negative; there are non-homogeneous examples of complex dimension 2, if one of the eigenvalues is zero. The problem of existence of Kahler metrics whose Ricci tensor has two distinct, constant eigenvalues is related to the celebrated (still open) Goldberg conjecture. Consequently, the irreducible homogeneous examples with negative eigenvalues give rise to complete, Einstein, strictly almost Kahler metrics of any even real dimension greater than 4.Comment: 18 pages; final version; accepted for publication in International Journal of Mathematic

3-quasi-Sasakian manifolds

In the present paper we carry on a systematic study of 3-quasi-Sasakian manifolds. In particular we prove that the three Reeb vector fields generate an involutive distribution determining a canonical totally geodesic and Riemannian foliation. Locally, the leaves of this foliation turn out to be Lie groups: either the orthogonal group or an abelian one. We show that 3-quasi-Sasakian manifolds have a well-defined rank, obtaining a rank-based classification. Furthermore, we prove a splitting theorem for these manifolds assuming the integrability of one of the almost product structures. Finally, we show that the vertical distribution is a minimum of the corrected energy.Comment: 17 pages, minor modifications, references update

Natural Diagonal Riemannian Almost Product and Para-Hermitian Cotangent Bundles

We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. We prove the characterization theorem for the natural diagonal (almost) para-K\"ahlerian structures on the total spaces of the cotangent bundle.Comment: 10 pages, will appear in Czechoslovak Mathematical Journa

CEACAM1 dampens antitumor immunity by down-regulating NKG2D ligand expression on tumor cells

By retaining NKG2D ligands within tumor cells, carcinoembryonic antigen–related cell adhesion molecule 1 (CEACAM1) facilitates tumor cell escape from NK cell–mediated cytolysis in vitro and in vivo

Riemannian submersions from almost contact metric manifolds

In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kaehler fibres.Comment: Abh. Math. Semin. Univ. Hamb., to appea

A comparative study of different model families for the constitutive simulation of viscous clays

The simulation of the viscous behavior of some clays is of high importance in many geotechnical problems. The literature offers a vast amount of constitutive models able to simulate the rate dependence observed on these materials. Although most of thesemodels are calibrated to very similar experimental observations and share similar definitions ofmaterial parameters, some discrepancies of their response have been detected, which are related to their mathematical formulations. In this work, the causes of these discrepancies are carefully studied. To that end, four different model families are analyzed, namely, nonstationary flow surface (NSFS) models, viscoplasticity with overstress function (OVP), viscoplasticity with Norton\u27s power law (NVP), and visco-hypoplasticity (VHP). For the sake of a fair comparison, single constitutive models using the same set of material parameters, and following other requirements, are developed for each model family. Numerical implementations of the four resulting models are performed. Their response at different tests are carefully analyzed through simulation examples and direct examination of their constitutive equations. The set includes some basic tests at isotropic stress states and others as responses envelopes, undrained creep rupture, and an oedometer test with loading, unloading-reloading, creep, and relaxation. The article is concluded with some remarks about the observed discrepancies of these model families

Killing-Yano tensors and some applications

The role of Killing and Killing-Yano tensors for studying the geodesic motion of the particle and the superparticle in a curved background is reviewed. Additionally the Papadopoulos list [74] for Killing-Yano tensors in G structures is reproduced by studying the torsion types these structures admit. The Papadopoulos list deals with groups G appearing in the Berger classification, and we enlarge the list by considering additional G structures which are not of the Berger type. Possible applications of these results in the study of supersymmetric particle actions and in the AdS/CFT correspondence are outlined.Comment: 36 pages, no figure