相关论文: Einstein, Levi-Civita, and Bianchi relations

We introduce the concept of singular values for the Riemann curvature tensor, a central mathematical tool in Einstein's theory of general relativity. We study the properties related to the singular values, and investigate five typical cases…

This paper discusses the extent to which one can determine the space-time metric from a knowledge of a certain subset of the (unparametrised) geodesics of its Levi-Civita connection, that is, from the experimental evidence of the…

The mathematical relations between certain classical Non-Riemannian gravity models and Einstein-Proca theories are discussed in details. We also show some relations with theories with scalar fields.

In his 1916's first paper on gravitational waves Einstein began to speculate on interactions between the principles of the old quantum theory and his theory of gravitation. With this contribution Einstein has stimulated a lot of similar…

We discuss Einstein's knowledge of projective geometry. We show that two pages of Einstein's Scratch Notebook from around 1912 with geometrical sketches can directly be associated with similar sketches in manuscript pages dating from his…

It is shown that the Levi-Civita metric can be obtained from a family of the Weyl metric, the Gamma metric, by taking the limit when the length of its Newtonian image source tends to infinity. In this process a relationship appears between…

We give a "soft" proof of Alberti's Luzin-type theorem in [1] (G. Alberti, A Lusintype theorem for gradients, J. Funct. Anal. 100 (1991)), using elementary geometric measure theory and topology. Applications to the $C^2$-rectifiability…

In 1924, Einstein received a short manuscript in the mail from the Indian physicist S.N. Bose. He quickly translated Bose's manuscript to German and submitted it to Zeitschrift f\"ur Physik. Within a few weeks, Einstein presented his own…

In his search for a unified field theory that could undercut quantum mechanics, Einstein considered five dimensional classical Kaluza-Klein theory. He studied this theory most intensively during the years 1938-1943. One of his primary…

A succinct chronology is given around Nov 1915, when the explicit field equations of General Relativity have been found. Evidence, unearthed by D.Wuensch, that a decisive document of Hilbert has been mutilated in recent years with the…

We show that small homogeneous solutions to the Einstein-Boltzmann-scalar field system exist globally towards the future and tend to the de Sitter solution in a suitable sense. More specifically, we assume that the spacetime is of Bianchi…

In 2024, after thirty years of research on this subject, I published a book entitled: \textit{Poincar\'{e}, Einstein and the discovery of special relativity. An end to the controversy} \cite{Ginoux2024}. In September 2025, Galina Weinstein…

The cosmological constant, usually named Lambda, was introduced by Einstein in 1917 and abandoned by him as his biggest "blunder". It currently seems to make a spectacular comeback in the framework of the new cosmological standard model.…

We show how an affine connection on a Riemannian manifold occurs naturally as a cochain in the complex for Leibniz cohomology of vector fields with coefficients in the adjoint representation. The Leibniz coboundary of the Levi-Civita…

We present a translation and analysis of a cosmic model published by Einstein in 1931. The paper, which is not widely known, features a model of a universe that undergoes an expansion followed by a contraction, quite different to his static…

Western thinking underwent a turning point between 1885 and 1925. Einstein in 1905 symbolizes the emblematic hinge of this change of direction. To find an equivalent phenomenon in the past we need to go back to the period from the XV…

Among the geniuses of mankind, Einstein was probably one of those who made more erroneous claims, and often changed his opinion during the years on important scientific subjects. However, it is important to bear in mind that his mistakes…

Graev introduced the construction of a convex polytope associated with a symmetric ternary relation. He showed that the number of left-invariant Einstein metrics on a homogeneous space under some conditions is no more than the normalized…

Einstein's reply to Weyl about the importance in General Relativity of the identity of the sources of spectral lines is well know. We show that, already in Special Relavitity, Einstein's definition of the unit of time from the frequency of…

Euler stressed the importance of hypotheses, which he thought were the only means of arriving at a certain knowledge of the physical causes, essential to establish the laws of physics. This thought was communicated to Emilie du Chatelet in…