The respectfully signed Dr Václav Hlavatý hereby politely requests that he be granted venia docendi at the local university in the field of "higher mathematics with a focus on differential geometry" based on the submitted thesis "Sur les courbes quasi asymptotiques".

The quasi-asymptotic curves (Bompiani) Q_{n+1} on a V_2 in V_n considered here are characterised by the fact that the osculating (ν + 1) vector of the curve contains the second direction of the V_2 at every point. The first chapter discusses: the general properties of Q_{n−1} on V_2 in V_n, the n−3 first curvatures of a Q_{n−1} on V_2 in S_n, the (n−2)th curvature, the Q_{n−k} on V_2 in S_n whose (n−k)th curvature vanishes, and the (n−k)th curvature of a Q_{n−k} on V_2 in V_n. On a V_2 in V_n, there is generally only Q_{n−1}, no Q_{n−k}, k > 1. The second chapter deals with the general properties of a Q′_{n′−1}, n′ = n−m+2 on V_m in V_n, the n′−3 first curvatures of a Q′_{n′−1} on V_m in S_n, and the (n−m+1)th curvature. On a V_m in V_n, there is generally only Q_{′n′−1}, no Q′_{n′−k}, k > 1.

Having examined the applicant's scientific activity, the Commission came to the conclusion that the applicant, after initial attempts, very soon worked his way up to an independent conception and processing of mathematical problems. He made extensive use of analogies that are offered in the new theory when comparing it with older results, but was led by them, which must be emphasised, to numerous results for which such analogies are lacking. This is good evidence that he has mastered the new theory well. At the same time, it can be observed - and this will become clear from the analyses carried out - how he gradually works his way up to increasingly general problems. Since his works extend into various branches of geometry and use rather complex analytical tools, it is justified to believe that his mathematical education is otherwise quite extensive and deep. The Commission came to the unanimous conclusion that the applicant meets very well the requirements that must be placed on an associate professor of mathematics, and proposes that 1) the applicant's habilitation thesis be approved, 2) the next parts of the habilitation procedure were moved on.

In this communication, the author has only addressed one application of the problem mentioned above: Given an n-dimensional curved projective space with an n-1 dimensional hypersurface X_{n-1} we need to find a projective normal of order 4 to X_{n-1} and, moreover, the projective connection induced in X_{n-1} by this normal. The normals found (explicitly) form a sheaf whose elements depend only on a numerical constant (cf. the case of a surface in 3-dimensional planar projective space!). We can explicitly construct a single projective normal of order 4, favoured by the fact that it is independent of the aforementioned constant. This normal induces a projective connection in X_{n-1}. If we are dealing with a non-holonomic hypersurface, a method analogous to this one gives us a projective normal of order 3.

It was October 1939 when I saw you, Professor Hlavatý, for the first time, at your first state lecture. You had a sarcastic smile and you were strict. However, your eyes gave me peace and you elaborated on my answers in a welcoming depth.

I met you after May 1945, during lectures and during the second state examination. Your smile was the same, you were just as strict. People around you told me about your uncompromising, brave stance during the German occupation, about the days and nights you spent on the barricades with a gun in your hand during the May Uprising.

... was a deputy in the Provisional National Assembly, which had a mandate from the summer of 1945 to the spring of 1946. He served as a deputy for only one month, from 10 April 1946, when he took over as a substitute for the deceased deputy for the National Socialist Party, Professor Klecand, until the end of his term on 16 May 1946. During his work in the cultural committee of the parliament, he spoke twice: he proposed the enactment of a four-year university study of statistics and actuarial mathematics, simultaneously at Charles University and at the Prague Technical University... ; he also spoke as a co-author of an interpellation in which he criticised the Minister of Education's school reform.

In a series of papers we shall establish an embedding X_m in a A_n (1 ≤ m < n, n ≥ 3). In this first paper some transformation laws are found which enable us a construction of a connection (which stamps our X_m to an A_m) as well as of higher connections which lead to a well-defined set of affine normal spaces of the A_m.

The smallest part of the work is taken up by lectures at the university. I lecture on differential geometry, linear geometry, algebraic geometry, the theory of relativity according to my books, something different every year, but it doesn't take up much of my time. More time is taken up by research level lectures, which I am invited to give almost all over America. My foreign students take up even more time ... However, my scientific work takes up the most time. Thank God, I still have something to say in science ...

I read in the article "Reflections on Gravity" (Aviation, Cosmonautics, 1965) that I am an American physicist of Czech origin. Naturally, I had to be naturalised when my homeland took away my citizenship, but I still feel like a Czech, not an American of Czech origin.

I took only one thing with me abroad, a souvenir of home: Dyk's poem "The Land Speaks". The mother land ends with the words: "I beg you, as your mother, to protect me, my son! Go, even if you are going to your death! If you leave me, I will not perish! If you leave me, it's you who will perish!" I carried that poem and carry it with me on all my journeys through life, and by reading it I pray to the lost homeland that I left without a fight. So I decided that I would use my work to promote the Czech name. ... I really seek to atone for the sin that I committed in my homeland when I left it. I know that if I had stayed, the fate of death would probably have awaited me, but that is no excuse for an honest person.

When Czechoslovak Society of Arts and Sciences in America was founded, my intention was to achieve two things and customise everything to them: 1) strong moral support on behalf of the homeland 2) the recognition of intellectual abilities of our exile at international forums. Unfortunately, others did not share my attitude. It was a disappointment for me. ... I resigned from the Executive Committee of the Czechoslovak Society of Arts and Sciences in America a year ago. They did not want to accept my decision.

The Czechoslovak Society of Arts and Sciences in America congress showed to our host country that we do not just beg but we are also able to give. It fulfilled its role as a professional scientific symposium and a valuable social link too. But no such gathering can replace the intellectual connection of those who need the intellectual sustenance regularly, not just once a year ...

He developed a nervous illness from overwork and employment, and perhaps this strain was the basis of his genius. Life was not easy for him, he often succumbed to pessimism, he did not believe in himself, he had to be encouraged or moderated at work, there were always fluctuations. Sometimes he was modest, sometimes self-confident, sometimes very stubborn, unpredictable and headstrong, which was ultimately his misfortune. He was honest, very sensitive and never wanted to hurt anyone, which he often failed to do, and his wit was sometimes cruel! He was immensely popular in society, he was always its centre, an outstanding figure; wherever he went, he had success. Despite all these successes, he was unhappy in his soul and that is perhaps why he also became a believer, not only because of the cosmic greatness he looked into.

Since I arrived, I have sent every book I have published to the Czechoslovak Academy of Sciences in Prague. Not only have they never thanked me (that would be asking too much from people who apparently have no sense of international courtesy), but they have never even acknowledged receipt of what I sent! I must admit that the Prague Academy is the only institution that behaves so rudely ...

His courage, his adventures, his linguistic prowess, his wit, and his charm - these are well known to his friends, as are his formidable mathematical powers and the brilliance of his mathematical technique.