The substituent effects on the ring-opening reaction of cyclobutene radical cations have been studied at the Becke3LYP/6-31G* level of theory. The effect on the reaction energies and activation energies of the concerted and stepwise pathways of electron-donating substituents such as methyl and methoxy as well as electron-withdrawing substituents such as nitrile and carboxaldehyde in the 3-posit...

The geometry of CR-submanifolds of Kaehler manifolds was initiated by Bejancu 1 and has been developed by 2–5 and others. They studied the geometry of CR-submanifolds with positive definite metric. Thus, this geometry may not be applicable to the other branches of mathematics and physics, where the metric is not necessarily definite. Moreover, because of growing importance of lightlike submanif...

We study half lightlike submanifold M of an indefinite transSasakian manifold such that its structure vector field is tangent to M . First we study the general theory for such half lightlike submanifolds. Next we prove some characterization theorems for half lightlike submanifolds of an indefinite generalized Sasakian space form.

Acknowledgements First and foremost I would like to thank my wife, Monika. Without her support and encouragement it is difficult to imagine completing this dissertation. I also owe a great deal to my thesis advisor Professor Blake Temple. Besides giving his support and encouragement, I have also benefitted greatly from his influence on my approach to research mathematics, and I look forward to ...

We obtain the expressions for sectional curvature, holomorphic sectional curvature, and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite Kaehler manifold. We discuss the boundedness of holomorphic sectional curvature of GCR-lightlike submanifolds of an indefinite complex space form. We establish a condition for a GCR-lightlike submanifold of an indefinite comple...

Copyright q 2011 Rakesh Kumar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We study mixed geodesic GCR-lightlike submanifolds of indefinite Sasakian manifolds and obtain some necessary and sufficient conditions for a GCR...

We give a causal version of Eisenhart's geodesic characterization of Newtonian dynamics. We emphasize the geometric, coordinate independent properties needed to express Eisenhart's theorem in light of modern studies on the Bargmann structures (lightlike dimensional reduction). The construction of the space metric, Coriolis 1-form and scalar potential through which the theorem is formulated is s...

‎We prove that there do not exist totally contact umbilical‎ ‎proper slant lightlike submanifolds of indefinite Sasakian manifolds other than totally contact geodesic‎ ‎proper slant lightlike submanifolds‎. ‎We also prove that there do‎ ‎not exist totally contact umbilical proper slant lightlike‎ ‎submanifolds of indefinite Sasakian space forms‎.

we obtain the expression of ricci tensor for a $gcr$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $gcr$-lightlike submanifold of anindefinite complex space form. moreover, we have proved that everyproper totally umbilical $gcr$-lightlike submanifold of anindefinite kaehler manifold is a totally geodesic $gcr$-lightlikesubmanifold.

We give a causal version of Eisenhart's geodesic characterization of classical mechanics. We emphasize the geometric, coordinate independent properties needed to express Eisenhart's theorem in light of modern studies on the Bargmann structures (lightlike dimensional reduction). The construction of the space metric, Coriolis 1-form and scalar potential through which the theorem is formulated is ...