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Context. Globular clusters host stars with chemical peculiarities. Theassociated helium enrichment is expected to affect the evolution of stars, ingeneral, and of low-mass stars, and in particular the progenitors of whitedwarfs (WDs). Aims. We investigate the effects of different initial heliumcontents on the properties of white dwarfs such as their masses, compositions,and the time since their formation. Results. In a globular cluster at a givenage, the He enrichment implies lower initial masses for stars at a given phase.Thus it leads to a decrease of the masses of white dwarfs reaching the coolingsequence. In addition the He enrichment increases the total mass and number ofwhite dwarfs and eventually allows the presence of He white dwarf from singleprogenitors. Conclusions. The low He enrichment determined in most globularclusters with different methods results in negligible effects on the whitedwarf properties. However, in the few globular clusters that display a high Heenrichment, this may significantly affect the characteristics of the whitedwarfs. In NGC 2808 and {\omega} Centauri the high He enrichment even leads tothe formation of He white dwarfs from single He-rich progenitors. Thereforeinvestigating the white dwarf mass domain in globular clusters with a high Heenrichment would provide an additional indirect way to measure and constrainthe He enrichment degree.

Evolution of long-lived globular cluster stars IV. Initial helium content and white-dwarf properties