scholarly journals How to construct all metric f-K-contact manifolds

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Oliver Goertsches ◽  
Eugenia Loiudice

Abstract We show that any compact metric f-K-contact, respectively S-manifold is obtained from a compact K-contact, respectively Sasakian manifold by an iteration of constructions of mapping tori, rotations, and type II deformations.

2011 ◽  
Vol 109 (1) ◽  
pp. 5 ◽  
Author(s):  
Selcen Yüksel Perktas ◽  
Erol Kiliç ◽  
Sadik Keles

In this paper we study the invariant and noninvariant hypersurfaces of $(1,1,1)$ almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively. We show that a noninvariant hypersurface of an $(1,1,1)$ almost contact manifold admits an almost product structure. We investigate hypersurfaces of affinely cosymplectic and normal $(1,1,1)$ almost contact manifolds. It is proved that a noninvariant hypersurface of a Lorentzian almost paracontact manifold is an almost product metric manifold. Some necessary and sufficient conditions have been given for a noninvariant hypersurface of a Lorentzian para-Sasakian manifold to be locally product manifold. We establish a Lorentzian para-Sasakian structure for an invariant hypersurface of a Lorentzian para-Sasakian manifold. Finally we give some examples for invariant and noninvariant hypersurfaces of a Lorentzian para-Sasakian manifold.


2004 ◽  
Vol 2004 (20) ◽  
pp. 1025-1034 ◽  
Author(s):  
Philippe Rukimbira

We prove that the dimension of the1-nullity distributionN(1)on a closed Sasakian manifoldMof ranklis at least equal to2l−1provided thatMhas an isolated closed characteristic. The result is then used to provide some examples ofk-contact manifolds which are not Sasakian. On a closed,2n+1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension ofN(1)is less than or equal ton+1orN(1)is the entire tangent bundleTM. In the latter case, the Sasakian manifoldMis isometric to a quotient of the Euclidean sphere under a finite group of isometries. We also point out some interactions betweenk-nullity, Weinstein conjecture, and minimal unit vector fields.


Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3885-3895 ◽  
Author(s):  
Hakan Taştan

We study Lagrangian submersions from Sasakian and Kenmotsu manifolds onto Riemannian manifolds. We prove that the horizontal distribution of a Lagrangian submersion from a Sasakian manifold onto a Riemannian manifold admitting vertical Reeb vector field is integrable, but the one admitting horizontal Reeb vector field is not. We also show that the horizontal distribution of a such submersion is integrable when the total manifold is Kenmotsu. Moreover, we give some applications of these results.


2002 ◽  
Vol 32 (8) ◽  
pp. 481-490 ◽  
Author(s):  
Gheorghe Pitiş

A complex subbundle of the normal bundle to an integral submanifold of the contact distribution in a Sasakian manifold is given. The geometry of this bundle is investigated and some results concerning its Chern classes are obtained.


Author(s):  
Krishnendu De

The object of the present paper is to obtain sufficient conditions  for a K-contact manifold to be a Sasakian manifold.


1994 ◽  
Vol 144 ◽  
pp. 283-284
Author(s):  
G. Maris ◽  
E. Tifrea

The type II solar radio bursts produced by a shock wave passing through the solar corona are one of the most frequently studied solar activity phenomena. The scientific interest in this type of phenomenon is due to the fact that the presence of this radio event in a solar flare is an almost certain indicator of a future geophysical effect. The origin of the shock waves which produce these bursts is not at all simple; besides the shocks which are generated as a result of a strong energy release during the impulsive phase of a flare, there are also the shocks generated by a coronal mass ejection or the shocks which appear in the interplanetary space due to the supplementary acceleration of the solar particles.


Author(s):  
Ronald S. Weinstein ◽  
N. Scott McNutt

The Type I simple cold block device was described by Bullivant and Ames in 1966 and represented the product of the first successful effort to simplify the equipment required to do sophisticated freeze-cleave techniques. Bullivant, Weinstein and Someda described the Type II device which is a modification of the Type I device and was developed as a collaborative effort at the Massachusetts General Hospital and the University of Auckland, New Zealand. The modifications reduced specimen contamination and provided controlled specimen warming for heat-etching of fracture faces. We have now tested the Mass. General Hospital version of the Type II device (called the “Type II-MGH device”) on a wide variety of biological specimens and have established temperature and pressure curves for routine heat-etching with the device.


Author(s):  
R. G. Gerrity ◽  
M. Richardson

Dogs were injected intravenously with E_. coli endotoxin (2 mg/kg), and lung samples were taken at 15 min., 1 hr. and 24 hrs. At 15 min., occlusion of pulmonary capillaries by degranulating platelets and polymorphonuclear leukocytes (PML) was evident (Fig. 1). Capillary endothelium was intact but endothelial damage in small arteries and arterioles, accompanied by intraalveolar hemorrhage, was frequent (Fig. 2). Sloughing of the surfactant layer from alveolar epithelium was evident (Fig. 1). At 1 hr., platelet-PML plugs were no longer seen in capillaries, the endothelium of which was often vacuolated (Fig. 3). Interstitial edema and destruction of alveolar epithelium were seen, and type II cells had discharged their granules into the alveoli (Fig. 4). At 24 hr. phagocytic PML's were frequent in peripheral alveoli, while centrally, alveoli and vessels were packed with fibrin thrombi and PML's (Fig. 5). In similar dogs rendered thrombocytopenic with anti-platelet serum, lung ultrastructure was similar to that of controls, although PML's were more frequently seen in capillaries in the former (Fig. 6).


Author(s):  
S. Laoussadi ◽  
A. Kahan ◽  
G. Aubouy ◽  
F. Delbarre

Several patients with Fabry's, Gaucher's diseases and hyperlipoproteinemia type II and with arthropatic manifestations were observed.As no histological explanation for these symptoms was available,an ultrastructural study of synovial tissue was done to establish an anatomoclinical relation.Material and Methods :synovial membrane samples were obtained by needle biopsies of the knee from three patients with arthropatic manifestations of each disease.They were fixed in 5% glutaraldehyde, postfixed in 1% osmium tetraoxyde and embedded in Epon 812. Thin sections coloured by uranyl acetate and lead citrate were observed with an Elmiskop I Siemens electron microscope.Two important phenomena were observed in synovial tissue:Specific patterns of each lipid storage disease,which are now well known.In all the three metabolic diseases, hydroxyapatite-like crystals were found. They are characterized by their intramitochondrial localization, without any relation with cristae,an anarchic disposition and a mean size of 550 A.Crystals may be found also free in the cytoplasm of synoviocytes Some micrographs suggest an evolution in four steps :a. mitochondria with only a few microcrystalsb. mitochondria stuffed with these structuresc. disruption of mitochondria membranesd. microcrystals appear free in the cytoplasm


Author(s):  
G. D. Gagne ◽  
M. F. Miller ◽  
D. A. Peterson

Experimental infection of chimpanzees with non-A, non-B hepatitis (NANB) or with delta agent hepatitis results in the appearance of characteristic cytoplasmic alterations in the hepatocytes. These alterations include spongelike inclusions (Type I), attached convoluted membranes (Type II), tubular structures (Type III), and microtubular aggregates (Type IV) (Fig. 1). Type I, II and III structures are, by association, believed to be derived from endoplasmic reticulum and may be morphogenetically related. Type IV structures are generally observed free in the cytoplasm but sometimes in the vicinity of type III structures. It is not known whether these structures are somehow involved in the replication and/or assembly of the putative NANB virus or whether they are simply nonspecific responses to cellular injury. When treated with uranyl acetate, type I, II and III structures stain intensely as if they might contain nucleic acids. If these structures do correspond to intermediates in the replication of a virus, one might expect them to contain DNA or RNA and the present study was undertaken to explore this possibility.


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