We present a catalogue of 1768 eclipsing binary stars (EBs) detected in the Large Magellanic Cloud (LMC) by the second generation of the EROS survey (hereinafter EROS-2); 493 of them are new discoveries located in outer regions (out of the central ba
r) of the LMC. These sources were originally included in a list of candidate classical Cepheids (CCs) extracted from the EROS-2 catalogue on the basis of the period (0.89 $<P_{EROS}<$15.85 days) versus luminosity ($13.39 < langle B_{EROS}rangle<17.82$ mag) diagram. After visual inspection of the light curves we reclassified them as eclipsing binaries. They have blue colours ($B_{EROS} - R_{EROS} < $ 0.2 mag) hence we classed them as hot eclipsing binaries (HEBs) containing hot massive components: main sequence (MS) stars or blue giants. We present $K_{rm s}$-band light curves for 999 binaries from our sample that have a counterpart in the VISTA near-infrared ESO public survey of the Magellanic Clouds system (VMC). We provide spectral classifications of 13 HEBs with existing spectroscopy. We divided our sample into contact-like binaries and detached/semi-detached systems based on both visual inspection and the parameters of the Fourier decomposition of the light curves and analysed the period-luminosity ($PL$) relations of the contact-like systems using the $R_{EROS}$ and $K_{rm s}$ magnitudes at maximum light. The contact-like binaries in our sample do not follow $PL$ relations. We analysed the sample of contact binaries from the OGLE III catalogue and confirmed that $PL_I$ and $PL_{K_{rm s}}$ sequences are defined only by eclipsing binaries containing a red giant component.
The VMC survey is obtaining multi-epoch photometry in the Ks band of the Magellanic System down to a limiting magnitude of Ks ~ 19.3 for individual epoch data. The observations are spaced in time such as to provide optimal sampling of the light curve
s for RR Lyrae stars and for Cepheids with periods up to 20-30 days. We present examples of the Ks-band light curves of Classical Cepheids and RR Lyrae stars we are obtaining from the VMC data and outline the strategy we put in place to measure distances and infer the System three-dimensional geometry from the variable stars. For this purpose the near-infrared Period-Luminosity, Period-Wesenheit, and Period-Luminosity-Colour relations of the system RR Lyrae stars and Cepheids are used. We extensively exploit the catalogues of the Magellanic Clouds variable stars provided by the EROS-2 and OGLE III/IV microlensing surveys. By combining these surveys we present the currently widest-area view of the Large Magellanic Cloud as captured by the galaxy Cepheids, RR Lyrae stars and binaries. This reveals the full extent of the main structures (bar/s - spiral arms) that have only been vaguely guessed before. Our work strengthens the case for a detailed study of the Large Magellanic Cloud three-dimensional geometry.
