# Marian Țarină

### Born: 15 August 1932 in Turda, Romania

Died: 31 May 1992 in Oradea, Romania

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**Marian Țarină**was born at Turda in August 1932. Turda is in Transylvania which had been part of Austro-Hungary up to the end of World War I but, in 1918, Transylvania had become part of Romania, and Turda with it. It was therefore part of Romania long before Țarină was born and the city of Turda was where he grew up. He attended the high school Regele Ferdinand (King Ferdinand), now named Mihai Viteazul (Michael the Brave) National College, in Turda, graduating in 1950. Then, he was admitted to the Faculty of Mathematics and Physics at the University of Cluj, being awarded a Magna Cum Laude Diploma in 1954. Upon graduation he was appointed as an assistant to the Chair of Geometry at the University of Cluj. He continued in this position until 1960 when he was promoted as a lecturer at Cluj. At the time Țarină became an assistant, there were two universities in Cluj, the Romanian University of Cluj which had been the King Ferdinand I University, was renamed Babeș University (after the Romanian natural scientist Victor Babeș) while the Hungarian University of Cluj was named the Bolyai University (after the mathematician János Bolyai). The two universities combined to become the Babeș-Bolyai University in 1959 so, after serving as an assistant in the Babeș University, Țarină became a lecturer in the Babeș-Bolyai University in 1960.

Under the guidance of academician Gheorghe Vrănceanu, he obtained his Ph.D. In Mathematics in 1964 from the University of Bucharest with a thesis entitled

*Partial Projective Spaces with Maximal Group of Motion*. He began publishing research articles, all written in Romanian, while working towards his doctorate. The first few of these articles are

*Plane pedal transformations and their application to non-euclidean geometry*(1963),

*Equiaffine subprojective spaces*(1964) and

*Subprojective spaces of order*

*n*- 3

*with maximum group of motions*(1964). The notion of a subprojective space had been introduced by Benjamin Fedorovich Kagan in 1933 and Vrănceanu had made a particular study of subprojective spaces of order

*n*- 2 in his book

*Lectures on differential geometry*(Romanian) (1951). Țarină used methods developed by his thesis advisor Vrănceanu to attack the case of subprojective spaces of order

*n*- 3 in his 1964 paper.

The entire didactical activity of Professor Marian Țarină was at the University of Cluj. He was promoted as "conferentiar", equivalent to a reader in the UK or associate professor in the US, in 1970. He obtained a full professorship when he was named to the Chair of Differential Geometry in 1990. Țarină taught many courses at Cluj on a variety of different topics such as: Differential Geometry, Fundamental Algebraic Topology, Symmetric Spaces, Lie Groups, Groups, and the History of Mathematics.

Throughout his career, Țarină published more than 50 research papers and presented almost 200 scientific communications. His research interests changed throughout his career. Fundamentals of geometry and non-Euclidean geometry were topics that interested him particularly between 1954 and 1957. From 1957 to 1967 his main interest was on Motion Groups in Riemann Spaces. He made a particular study of Recurrent Spaces for the five years following 1965, although he returned to the topic in 1980-81. He studied

*G*-structures on Differentiable Manifolds from around 1971 to 1980. He studied Invariant Connections from 1980 to 1984 and Finsler Spaces and generalisations from 1984 to 1992. Here are examples of papers, one on each of these topics, with a brief comment:

**Motion Groups in Riemann Spaces.**

**Paper:**

*On the mobility of a space*(1965).

*A*_{n}without torsion which admits fields of parallel vectors**Comment:**Starting from the fact that there are some general relations between conditions under which a space

*A*

_{n}with an affine connection without torsion possesses a group of motions or fields of parallel vectors, Țarină considers this problem for different kinds of spaces, known to have maximal groups of motions.

**Recurrent Spaces.**

**Paper:**

*Spaces*

*V*

_{n}

*with recurrent projective curvature*(1969).

**Comment:**In this note, Țarină discusses a generalisation of the projective and the conformal equivalence of connections on a manifold. The main result of the first section is a formula relating the curvature of two connections which are equivalent in the sense he defines in the paper. The second section discusses the notion of an admissible morphism, and the corresponding transformation of equivalent connections.

**G-structures on Differentiable Manifolds.**

**Paper:**

*Equivalent connections on G-structures of order 2*(1980).

**Comment:**In this note, Țarină discusses a generalisation of the projective and the conformal equivalence of connections on a manifold.

**Invariant Connections.**

**Paper:**

*Invariant connections*(1981).

**Comment:**In this paper, Țarină gives a few ways of defining invariant connections in principal fibre bundles and establishes some properties about the order of invariant connections.

**Finsler Spaces and generalisations.**

**Paper:**

*Finsler connections and associated algebras*(1982).

**Comment:**Țarină writes, "Many geometric objects in the theory of Finsler spaces present an obvious analogy with the case of linear connections. This is the case for the problems of algebras associated with some classes of Finsler connexions, which we consider here."

*Carl Friedrich Gauss (1777-1855) as a precursor of the topology*(1977),

*Development of geometry in the period of the French Revolution*(1979) and

*The ideas of the Appendix-the chief work of János Bolyai*(1979).

Țarină unexpected died in May 1992 at Oradea in his sixtieth year. Andrica Dorin, the author of [1] and co-author of [3], writes in [1]:-

A Symposium in Geometry was organized on the occasion of the 190Lectures by Professor Marian Țarină at the University of Cluj were always marked by their scientific rigour and clarity of exposition. He lectured on geometry, differential geometry, foundations of geometry, topology, algebraic topology, symmetric spaces, Lie groups, foundations of mathematics, history of mathematics, some of which were published and became relevant references to other courses or books in our country[Romania]. I had the wonderful opportunity to be a student of Professor Dr Marian Țarină, both during college and later when he directed my doctoral studies. My contacts with Marian Țarină showed me the special human qualities of that excellent mathematician: warmth, modesty, and humour. My memories of Professor Marian Țarină will remain alive throughout my life.

^{th}anniversary of Janos Bolyai and of the 60

^{th}anniversary of Marian Țarină at Babeș-Bolyai University in Cluj-Napoca in 1993. The regional Romanian school mathematics and computer science competition is now named the 'Marian Țarină competition'.

**Article by:** *J J O'Connor* and *E F Robertson*

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**List of References** (3 books/articles)

**Mathematicians born in the same country**

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