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97. Guido Magnano, Leszek M. Soko這wski Can the local stressenergy conservation laws be derived solely from field equations? Gen. Rel. Grav., vol. 30, pp. 12811288 (1998). [abstract] [preprint]  Abstract: According to a recent suggestion [1], the energymomentum tensor for gravitating fields can be computed through a suitable rearrangement of the matter field equations, without relying on the variational definition. We show that the property observed by Accioly et al. in [1] is the consequence of a general identity, which follows from the covariance of the matter Lagrangian in much the same way as (generalized) Bianchi identities follow from the covariance of the purely gravitational Lagrangian. However, we also show that only in particular cases can this identity be used to obtain the actual form of the stressenergy tensor, while in general the method leads to ambiguities and possibly to wrong results. Moreover, in nontrivial cases the computations turn out to be more difficult than the standard variational technique.  98. Marek Szydlowski, Andrzej J. Maciejewski, Jacek Guzik Dynamical Trajectories of Simple Mechanical Systems as Geodesics in Space with an Extra Dimension Int. J. of Theor. Phys., vol. 37, p. 1569 (1998). [preprint] [journal]  Abstract:
 99. Zdzislaw Pogoda, Leszek M. Soko這wski Does Mathematics Distinguish Certain Dimensions of Spaces? Part II. The American Mathematical Monthly, vol. 105, pp. 456463 (1998). [journal]  Abstract: Abstract  100. Zdzislaw Pogoda, Leszek M. Soko這wski Does Mathematics Distinguish Certain Dimensions of Spaces? Part I. The American Mathematical Monthly, vol. 104, pp. 860869 (1997). [journal]  Abstract: Abstract  101. Marco Litterio, Leszek M. Soko這wski, Zdzis豉w A. Golda, Luca Amendola, Andrzej Dyrek Anisotropic inflation from extra dimensions Phys. Lett., vol. B382, pp. 4552 (1996). [abstract] [preprint] [journal]  Abstract: Vacuum multidimensional cosmological models with internal spaces being compact $n$dimensional Lie group manifolds are considered. Products of 3spheres and $SU(3)$ manifold (a novelty in cosmology) are studied. It turns out that the dynamical evolution of the internal space drives (powerlaw) inflation in the external world. This inflationary solution brings two extra bonuses: 1) it is an attractor in phase space (no finetuning required); 2) it is determined by the Lie group space solely and not by any arbitrary inflaton potentials. Only scalar fields representing the anisotropic scale factors of the internal space appears in the four dimensions. The size of the volume of the internal space at the end of inflation is compatible with observational constraints. This simple and natural model can be completed by some extendedinflationlike mechanism that ends the inflationary evolution.  102. Zdzis豉w A. Golda, Marco Litterio, Leszek M. Soko這wski, Luca Amendola, Andrzej Dyrek Pure Geometrical Evolution of the Multidimensional Universe Ann. Phys. , vol. 248, pp. 246285 (1996). [abstract] [journal]  Abstract: An exhaustive qualitative analysis of cosmological evolution for some multidimensional universes is given. The internal space is taken to be a compact Lie group Riemannian manifold. The space is generically anisotropic; i.e., its cosmological evolution is described by its (timedependent) volume, the dilaton, and by relative anisotropic deformation factors representing the shear of the internal dimensions during the evolution. Neither the internal space nor its subspaces need to be Einstein spaces. The total spacetime is empty, and the cosmic evolution of the external, fourdimensional world is driven by the geometric ``matter'' consisting of the dilaton and of the deformation factors. Since little is known about any form of matter in the extra dimensions, we do not introduce any {\it ad hoc\/} matter content of the Universe. We derive the fourdimensional Einstein field equations (with a cosmological term) for these geometric sources in full generality, i.e., for any compact Lie group. A detailed analysis is done for some specific internal geometries: products of 3spheres, and $SU$(3) space. Asymptotic solutions exhibit power law inflation along with a process of full or partial isotropization. For the $SU$(3) space all the deformation factors tend to a common value, whereas in the case of $S^3$'s each sphere isotropizes separately.  
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